This document proposes a novel nonadditive collaborative filtering approach for recommender systems that use multicriteria ratings. It introduces traditional collaborative filtering approaches that use single-criterion or overall ratings. It then describes two existing approaches for multicriteria ratings - the similarity-based approach and the aggregation-function based approach. The key contribution is a new approach that uses the Choquet integral, a nonadditive technique from multicriteria decision making, to aggregate multicriteria ratings for recommending unrated items instead of the traditional weighted average method.
Ontological and clustering approach for content based recommendation systemsvikramadityajakkula
This document proposes a novel content-based recommendation system that uses ontological graphs and dynamic weighted ranking. It builds an adaptive ranking mechanism based on user selections and preferences to improve recommendation accuracy over time. The system segments data into ontological groups and identifies relationships between entities. It then calculates similarity between entities using feature vectors and ranks entities based on weights assigned to their connections in the ontological graph. These weights are updated dynamically based on user feedback to personalize recommendations for each user. The paper describes testing this approach in a recipe recommendation tool called RecipeMiner, which produced coherent recommendations that adapted to user preferences.
A LOCATION-BASED RECOMMENDER SYSTEM FRAMEWORK TO IMPROVE ACCURACY IN USERBASE...ijcsa
This document proposes a framework to improve the accuracy of recommendations in collaborative filtering recommender systems by considering users' locations. The framework enhances traditional collaborative filtering in several ways: 1) It increases the similarity score of users located in the same place as the active user; 2) It filters peers to remove non-related users; 3) It selects the top peers and recommends items based on those peers' ratings. The framework aims to provide more local recommendations by incorporating geographic location data throughout the recommendation process.
An Adaptive Framework for Enhancing Recommendation Using Hybrid Techniqueijcsit
Recommender systems provide useful recommendations to a collection of users for items or products that
might be of concern or interest to them. Several techniques have been proposed for recommendation such
as collaborative filtering, content-based, knowledge-based, and demographic filtering. Each of these
techniques suffers from scalability, data sparsity, and cold-start problems when applied individually
resulting in poor recommendations. This paper proposes an adaptive hybrid recommender system that
combines multiple techniques together to achieve some synergy between them. Collaborative filtering and
demographic techniques are combined in a weighted linear formula. Different experiments applied using
movieLen dataset confirm that the proposed adaptable hybrid framework outperforms the weaknesses
resulted when using traditional recommendation techniques.
IRJET- Book Recommendation System using Item Based Collaborative FilteringIRJET Journal
This document describes an item-based collaborative filtering approach for a book recommendation system. It discusses different recommendation system techniques including collaborative filtering, content-based filtering, and hybrid filtering. It then focuses on item-based collaborative filtering, explaining how it calculates item similarities using adjusted cosine similarity and makes predictions using weighted sums. The document tests the approach on the Goodbooks10k dataset and evaluates it using mean absolute error, finding lower error rates with more neighbor items. In conclusion, item-based collaborative filtering is an effective approach for book recommendations.
SIMILARITY MEASURES FOR RECOMMENDER SYSTEMS: A COMPARATIVE STUDYJournal For Research
Recommender Systems have the ability to guide the users in a personalized way to interesting items in a large space of possible options. They have fundamental applications in e-commerce and information retrieval, providing suggestion that prune large information spaces so that users are directed towards those items that best meets the needs and preferences. A variety of approaches have been proposed but collaborative filtering has been the most popular and widely used which makes use of various similarity measures to calculate the similarity. Collaborative Filtering takes the user feedback in the form of ratings in an application area and uses it to find similarities and differences between user profiles to generate recommendations. Collaborative Filtering makes use of various similarity measures to calculate the similarity or difference between the users. This paper provides an overview on few important similarity measures that are currently being used. Different similarity measures provide different results against same input parameters. So, to understand how various similarity measures behave when they are put in different contexts but with same input, few observations are made. This paper also provides a comparison graph to help understand the results of different similarity measures.
A Hybrid Approach for Personalized Recommender System Using Weighted TFIDF on...Editor IJCATR
Recommender systems are gaining a great popularity with the emergence of e-commerce and social media on the internet. These recommender systems enable users’ access products or services that they would otherwise not be aware of due to the wealth of information on the internet. Two traditional methods used to develop recommender systems are content-based and collaborative filtering. While both methods have their strengths, they also have weaknesses; such as sparsity, new item and new user problem that leads to poor recommendation quality. Some of these weaknesses can be overcome by combining two or more methods to form a hybrid recommender system. This paper deals with issues related to the design and evaluation of a personalized hybrid recommender system that combines content-based and collaborative filtering methods to improve the precision of recommendation. Experiments done using MovieLens dataset shows the personalized hybrid recommender system outperforms the two traditional methods implemented separately.
This document summarizes key considerations for evaluating collaborative filtering recommender systems. It discusses the user tasks being evaluated, types of analysis and datasets used, ways to measure prediction quality and other attributes, and how to evaluate the overall system from the user perspective. It presents empirical results showing that different accuracy metrics on one dataset collapsed into three groups that were either strongly or uncorrelated. The document aims to help researchers and practitioners properly evaluate and compare recommender system algorithms.
This document summarizes a research paper that proposes a novel approach for dynamic personalized recommendation. It utilizes information from user ratings and profiles to develop dynamic features that describe user preferences over multiple phases of interest. An adaptive weighting algorithm then makes recommendations by weighting these dynamic features based on the amount of rating data available. The proposed approach was tested on public datasets and performed well for dynamic recommendation compared to existing algorithms.
Ontological and clustering approach for content based recommendation systemsvikramadityajakkula
This document proposes a novel content-based recommendation system that uses ontological graphs and dynamic weighted ranking. It builds an adaptive ranking mechanism based on user selections and preferences to improve recommendation accuracy over time. The system segments data into ontological groups and identifies relationships between entities. It then calculates similarity between entities using feature vectors and ranks entities based on weights assigned to their connections in the ontological graph. These weights are updated dynamically based on user feedback to personalize recommendations for each user. The paper describes testing this approach in a recipe recommendation tool called RecipeMiner, which produced coherent recommendations that adapted to user preferences.
A LOCATION-BASED RECOMMENDER SYSTEM FRAMEWORK TO IMPROVE ACCURACY IN USERBASE...ijcsa
This document proposes a framework to improve the accuracy of recommendations in collaborative filtering recommender systems by considering users' locations. The framework enhances traditional collaborative filtering in several ways: 1) It increases the similarity score of users located in the same place as the active user; 2) It filters peers to remove non-related users; 3) It selects the top peers and recommends items based on those peers' ratings. The framework aims to provide more local recommendations by incorporating geographic location data throughout the recommendation process.
An Adaptive Framework for Enhancing Recommendation Using Hybrid Techniqueijcsit
Recommender systems provide useful recommendations to a collection of users for items or products that
might be of concern or interest to them. Several techniques have been proposed for recommendation such
as collaborative filtering, content-based, knowledge-based, and demographic filtering. Each of these
techniques suffers from scalability, data sparsity, and cold-start problems when applied individually
resulting in poor recommendations. This paper proposes an adaptive hybrid recommender system that
combines multiple techniques together to achieve some synergy between them. Collaborative filtering and
demographic techniques are combined in a weighted linear formula. Different experiments applied using
movieLen dataset confirm that the proposed adaptable hybrid framework outperforms the weaknesses
resulted when using traditional recommendation techniques.
IRJET- Book Recommendation System using Item Based Collaborative FilteringIRJET Journal
This document describes an item-based collaborative filtering approach for a book recommendation system. It discusses different recommendation system techniques including collaborative filtering, content-based filtering, and hybrid filtering. It then focuses on item-based collaborative filtering, explaining how it calculates item similarities using adjusted cosine similarity and makes predictions using weighted sums. The document tests the approach on the Goodbooks10k dataset and evaluates it using mean absolute error, finding lower error rates with more neighbor items. In conclusion, item-based collaborative filtering is an effective approach for book recommendations.
SIMILARITY MEASURES FOR RECOMMENDER SYSTEMS: A COMPARATIVE STUDYJournal For Research
Recommender Systems have the ability to guide the users in a personalized way to interesting items in a large space of possible options. They have fundamental applications in e-commerce and information retrieval, providing suggestion that prune large information spaces so that users are directed towards those items that best meets the needs and preferences. A variety of approaches have been proposed but collaborative filtering has been the most popular and widely used which makes use of various similarity measures to calculate the similarity. Collaborative Filtering takes the user feedback in the form of ratings in an application area and uses it to find similarities and differences between user profiles to generate recommendations. Collaborative Filtering makes use of various similarity measures to calculate the similarity or difference between the users. This paper provides an overview on few important similarity measures that are currently being used. Different similarity measures provide different results against same input parameters. So, to understand how various similarity measures behave when they are put in different contexts but with same input, few observations are made. This paper also provides a comparison graph to help understand the results of different similarity measures.
A Hybrid Approach for Personalized Recommender System Using Weighted TFIDF on...Editor IJCATR
Recommender systems are gaining a great popularity with the emergence of e-commerce and social media on the internet. These recommender systems enable users’ access products or services that they would otherwise not be aware of due to the wealth of information on the internet. Two traditional methods used to develop recommender systems are content-based and collaborative filtering. While both methods have their strengths, they also have weaknesses; such as sparsity, new item and new user problem that leads to poor recommendation quality. Some of these weaknesses can be overcome by combining two or more methods to form a hybrid recommender system. This paper deals with issues related to the design and evaluation of a personalized hybrid recommender system that combines content-based and collaborative filtering methods to improve the precision of recommendation. Experiments done using MovieLens dataset shows the personalized hybrid recommender system outperforms the two traditional methods implemented separately.
This document summarizes key considerations for evaluating collaborative filtering recommender systems. It discusses the user tasks being evaluated, types of analysis and datasets used, ways to measure prediction quality and other attributes, and how to evaluate the overall system from the user perspective. It presents empirical results showing that different accuracy metrics on one dataset collapsed into three groups that were either strongly or uncorrelated. The document aims to help researchers and practitioners properly evaluate and compare recommender system algorithms.
This document summarizes a research paper that proposes a novel approach for dynamic personalized recommendation. It utilizes information from user ratings and profiles to develop dynamic features that describe user preferences over multiple phases of interest. An adaptive weighting algorithm then makes recommendations by weighting these dynamic features based on the amount of rating data available. The proposed approach was tested on public datasets and performed well for dynamic recommendation compared to existing algorithms.
Context Based Classification of Reviews Using Association Rule Mining, Fuzzy ...journalBEEI
The Internet has facilitated the growth of recommendation system owing to the ease of sharing customer experiences online. It is a challenging task to summarize and streamline the online textual reviews. In this paper, we propose a new framework called Fuzzy based contextual recommendation system. For classification of customer reviews we extract the information from the reviews based on the context given by users. We use text mining techniques to tag the review and extract context. Then we find out the relationship between the contexts from the ontological database. We incorporate fuzzy based semantic analyzer to find the relationship between the review and the context when they are not found therein. The sentence based classification predicts the relevant reviews, whereas the fuzzy based context method predicts the relevant instances among the relevant reviews. Textual analysis is carried out with the combination of association rules and ontology mining. The relationship between review and their context is compared using the semantic analyzer which is based on the fuzzy rules.
A REVIEW PAPER ON BFO AND PSO BASED MOVIE RECOMMENDATION SYSTEM | J4RV4I1015Journal For Research
Recommendation system plays important role in Internet world and used in many applications. It has created the collection of many application, created global village and growth for numerous information. This paper represents the overview of Approaches and techniques generated in recommendation system. Recommendation system is categorized in three classes: Collaborative Filtering, Content based and hybrid based Approach. This paper classifies collaborative filtering in two types: Memory based and Model based Recommendation .The paper elaborates these approaches and their techniques with their limitations. The result of our system provides much better recommendations to users because it enables the users to understand the relation between their emotional states and the recommended movies.
Collaborative filtering is a technique used in recommender systems to predict a user's preferences based on other similar users' preferences. It involves collecting ratings data from users, calculating similarities between users or items, and making recommendations. Common approaches include user-user collaborative filtering, item-item collaborative filtering, and probabilistic matrix factorization. Recommender systems are evaluated both offline using metrics like MAE and RMSE, and through online user testing.
Analysing the performance of Recommendation System using different similarity...IRJET Journal
The document analyzes the performance of different similarity metrics used in recommendation systems, including Pearson correlation, cosine similarity, Jaccard coefficient, mean squared difference, and singular value decomposition. It finds that the Jaccard similarity metric produces better accuracy and less time complexity compared to Pearson correlation and cosine similarity when applied to the Movielens 100k dataset. The document also provides an overview of recommendation system types such as content-based, collaborative filtering, and hybrid systems, as well as collaborative filtering approaches like user-to-user and item-to-item.
Entropy-weighted similarity measures for collaborative recommender systems.pdfMalim Siregar
The document describes a proposed method for improving collaborative recommender systems by incorporating information entropy into traditional similarity measures. Specifically, it defines entropy for each item based on the probability distribution of user ratings for that item. It then incorporates the item entropy weights into Pearson correlation and cosine similarity measures to calculate similarity between users. Experiments on MovieLens and BookCrossing datasets show the proposed entropy-weighted measures improve prediction accuracy over traditional measures on MovieLens, but provide little benefit for the sparser BookCrossing dataset.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IRJET- Fatigue Analysis of Offshore Steel StructuresIRJET Journal
This document proposes a hybrid book recommender system that uses genetic algorithms. It describes a model that integrates the outputs of different recommender approaches using genetic algorithms to optimize weight vectors. The fitness function evaluates accuracy by comparing the combined results to actual ratings. An individual selection strategy applies simulated annealing concepts to avoid premature convergence. Experiments showed the proposed hybrid model has higher accuracy than traditional methods.
IRJET- Web based Hybrid Book Recommender System using Genetic AlgorithmIRJET Journal
The document proposes a hybrid book recommender system that uses genetic algorithms to integrate the outputs of different recommender approaches, including collaborative and content-based filtering. It describes using genetic algorithms to learn optimal weights to combine the results from various recommenders to improve recommendation accuracy. Experiments show the proposed hybrid genetic algorithm approach achieves better performance than traditional recommendation methods.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Iso9126 based software quality evaluation using choquet integral ijseajournal
This document summarizes a research paper that evaluates software quality using the Choquet integral approach. The paper introduces aggregation functions commonly used to evaluate software quality, such as the arithmetic mean and weighted arithmetic mean. It then presents the Choquet integral as a new approach that considers interactions among quality criteria. The paper applies the Choquet integral to evaluate software alternatives based on ISO 9126 quality attributes, using real data from case studies. Evaluation results are compared to other aggregation methods to demonstrate the Choquet integral's ability to model interactions among criteria.
The document discusses movie recommendation systems. It describes how recommendation systems work by predicting a user's rating or preference for an item based on their past ratings and preferences. It outlines several methods used in recommendation systems, including collaborative filtering, content-based filtering, and hybrid systems. It also discusses some specific types of recommendation systems like multi-criteria, risk-aware, and mobile recommender systems. The document provides examples of companies that use recommendation systems and classifications and techniques used to develop these systems.
RANKING BASED ON COLLABORATIVE FEATURE-WEIGHTING APPLIED TO THE RECOMMENDATIO...ijaia
Current research on recommendation systems focuses on optimization and evaluation of the quality
of ranked recommended results. One of the most common approaches used in digital paper
libraries to present and recommend relevant search results, is ranking the papers based on their
features. However, feature utility or relevance varies greatly from highly relevant to less relevant,
and redundant. Departing from the existing recommendation systems, in which all item features
are considered to be equally important, this study presents the initial development of an approach
to feature weighting with the goal of obtaining a novel recommendation method in which features
which are more effective have a higher contribution/weight to the ranking process. Furthermore,
it focuses on obtaining ranking of results returned by a query through a collaborative weighting
procedure carried out by human users. The collaborative feature-weighting procedure is shown to
be incremental, which in turn leads to an incremental approach to feature-based similarity evaluation.
The obtained system is then evaluated using Normalized Discounted Cumulative Gain
(NDCG) with respect to a crowd-sourced ranked results. Comparison between the performance of
the proposed and Ranking SVM methods shows that the overall ranking accuracy of the proposed
approach outperforms the ranking accuracy of Ranking SVM method.
Personalized recommendation for cold start usersIRJET Journal
The document discusses personalized recommendation methods for cold start users. It describes several recommendation techniques including content-based filtering, collaborative filtering, and hybrid recommendation. It also discusses challenges like cold start problems and data sparsity. Trust-based recommendation systems are described that incorporate social relationships between users. Matrix factorization techniques are discussed for modeling user-item interactions and incorporating additional contextual factors. The use of probabilistic matrix factorization models to address cold start and sparsity problems is also covered.
IRJET- Analysis of Rating Difference and User InterestIRJET Journal
This document summarizes a research paper that proposes a collaborative filtering recommendation algorithm that incorporates rating differences and user interests. It first adds a rating difference factor to the traditional collaborative filtering algorithm. It then calculates user interests based on item attributes and the similarity between user interests. Recommendations are made by weighting user rating differences and interest similarities. The proposed algorithm is shown to reduce error rates and improve accuracy compared to traditional collaborative filtering.
The document proposes a framework called TRUE-REPUTATION to calculate trustworthy product reputations from online ratings. It addresses the problem of "false reputations" which can occur when some ratings are intentionally unfair. TRUE-REPUTATION iteratively computes a rating's confidence based on the user's activity, objectivity and consistency, and adjusts the product's reputation accordingly. It determines these factors by analyzing characteristics of reliable information from previous research. The goal is to reduce the impact of unfair ratings while including all ratings to avoid excluding normal users.
This document summarizes several research papers on improving recommendation systems using item-based collaborative filtering approaches. It discusses challenges with traditional collaborative filtering like data sparsity and scalability. It then summarizes various item-based recommendation algorithms that analyze item relationships to indirectly compute recommendations. These include item-item similarity techniques like cosine similarity and adjusting for average ratings. The document also reviews literature on combining item categories and interestingness measures to improve accuracy. Overall, it analyzes different item-based collaborative filtering techniques to address challenges and provide high quality, personalized recommendations at scale.
This document outlines a proposed framework called TKmeans++ for identifying grey sheep users (GSU) and recommending items to them based on trust relations. The framework has two phases: a GSU identification phase that calculates user weights based on similarity, influence, and trust to assign users to clusters, and a recommendation phase that recommends top items to a GSU based on items positively rated by other GSU. An experimental study on the Epinions dataset shows TKmeans++ outperforms other clustering algorithms on MAE and coverage metrics for recommending to GSU. Future work could explore matrix factorization approaches or combining clustering and matrix factorization.
IRJET- Review on Different Recommendation Techniques for GRS in Online Social...IRJET Journal
This document reviews different recommendation techniques for group recommender systems (GRS) in online social networks. It discusses traditional recommender approaches like content-based filtering and collaborative filtering. It also reviews related work applying opinion dynamics models and weight matrices to GRS. The document concludes that using a smart weights matrix to consider relationships between group members' preferences in a recommendation process improves aggregation and ensures consensus, providing the best way to recommend items to a complete group.
Tourism Based Hybrid Recommendation SystemIRJET Journal
This paper proposes a hybrid tourism recommendation system that combines collaborative filtering, content-based filtering, and aspect-based sentiment analysis to improve accuracy and address cold start problems. The system analyzes user ratings and reviews to predict ratings for other tourism packages. It stores ratings, reviews, and sentiment information in a database to enhance recommendations. Results showed the hybrid approach increased efficiency over conventional methods. Future work could include testing on additional datasets and expanding the system.
Entering College Essay. Top 10 Tips For College AdmissNat Rice
The document summarizes the discovery of a new species, Alborum Plumae, found in Mount Kosciuszko National Park in Australia. Dr. Ella Beard discovered small feathered creatures perfectly camouflaged as snow lumps on tree branches. Early analysis finds they spend most of their time stationary to avoid detection, using their wings only for escaping predators. While sharing traits with birds like down insulation and wing-aided flight, further research is needed to determine their exact taxonomic classification.
006 Essay Example First Paragraph In An ThatsnoNat Rice
The document summarizes racism depicted in two novels by John Updike: Rabbit Run and Rabbit Redux. It notes that both books show racism as an issue, with characters making racist comments about black people. Specific quotes are presented that demonstrate racist language used by characters towards black individuals. The racism portrayed is less extreme in Rabbit Redux compared to Rabbit Run. Overall, the document analyzes how Updike explores themes of racism through his famous character Harry Rabbit and the other characters in these two novels from his Rabbit series.
More Related Content
Similar to A Novel Nonadditive Collaborative-Filtering Approach Using Multicriteria Ratings
Context Based Classification of Reviews Using Association Rule Mining, Fuzzy ...journalBEEI
The Internet has facilitated the growth of recommendation system owing to the ease of sharing customer experiences online. It is a challenging task to summarize and streamline the online textual reviews. In this paper, we propose a new framework called Fuzzy based contextual recommendation system. For classification of customer reviews we extract the information from the reviews based on the context given by users. We use text mining techniques to tag the review and extract context. Then we find out the relationship between the contexts from the ontological database. We incorporate fuzzy based semantic analyzer to find the relationship between the review and the context when they are not found therein. The sentence based classification predicts the relevant reviews, whereas the fuzzy based context method predicts the relevant instances among the relevant reviews. Textual analysis is carried out with the combination of association rules and ontology mining. The relationship between review and their context is compared using the semantic analyzer which is based on the fuzzy rules.
A REVIEW PAPER ON BFO AND PSO BASED MOVIE RECOMMENDATION SYSTEM | J4RV4I1015Journal For Research
Recommendation system plays important role in Internet world and used in many applications. It has created the collection of many application, created global village and growth for numerous information. This paper represents the overview of Approaches and techniques generated in recommendation system. Recommendation system is categorized in three classes: Collaborative Filtering, Content based and hybrid based Approach. This paper classifies collaborative filtering in two types: Memory based and Model based Recommendation .The paper elaborates these approaches and their techniques with their limitations. The result of our system provides much better recommendations to users because it enables the users to understand the relation between their emotional states and the recommended movies.
Collaborative filtering is a technique used in recommender systems to predict a user's preferences based on other similar users' preferences. It involves collecting ratings data from users, calculating similarities between users or items, and making recommendations. Common approaches include user-user collaborative filtering, item-item collaborative filtering, and probabilistic matrix factorization. Recommender systems are evaluated both offline using metrics like MAE and RMSE, and through online user testing.
Analysing the performance of Recommendation System using different similarity...IRJET Journal
The document analyzes the performance of different similarity metrics used in recommendation systems, including Pearson correlation, cosine similarity, Jaccard coefficient, mean squared difference, and singular value decomposition. It finds that the Jaccard similarity metric produces better accuracy and less time complexity compared to Pearson correlation and cosine similarity when applied to the Movielens 100k dataset. The document also provides an overview of recommendation system types such as content-based, collaborative filtering, and hybrid systems, as well as collaborative filtering approaches like user-to-user and item-to-item.
Entropy-weighted similarity measures for collaborative recommender systems.pdfMalim Siregar
The document describes a proposed method for improving collaborative recommender systems by incorporating information entropy into traditional similarity measures. Specifically, it defines entropy for each item based on the probability distribution of user ratings for that item. It then incorporates the item entropy weights into Pearson correlation and cosine similarity measures to calculate similarity between users. Experiments on MovieLens and BookCrossing datasets show the proposed entropy-weighted measures improve prediction accuracy over traditional measures on MovieLens, but provide little benefit for the sparser BookCrossing dataset.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IRJET- Fatigue Analysis of Offshore Steel StructuresIRJET Journal
This document proposes a hybrid book recommender system that uses genetic algorithms. It describes a model that integrates the outputs of different recommender approaches using genetic algorithms to optimize weight vectors. The fitness function evaluates accuracy by comparing the combined results to actual ratings. An individual selection strategy applies simulated annealing concepts to avoid premature convergence. Experiments showed the proposed hybrid model has higher accuracy than traditional methods.
IRJET- Web based Hybrid Book Recommender System using Genetic AlgorithmIRJET Journal
The document proposes a hybrid book recommender system that uses genetic algorithms to integrate the outputs of different recommender approaches, including collaborative and content-based filtering. It describes using genetic algorithms to learn optimal weights to combine the results from various recommenders to improve recommendation accuracy. Experiments show the proposed hybrid genetic algorithm approach achieves better performance than traditional recommendation methods.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Iso9126 based software quality evaluation using choquet integral ijseajournal
This document summarizes a research paper that evaluates software quality using the Choquet integral approach. The paper introduces aggregation functions commonly used to evaluate software quality, such as the arithmetic mean and weighted arithmetic mean. It then presents the Choquet integral as a new approach that considers interactions among quality criteria. The paper applies the Choquet integral to evaluate software alternatives based on ISO 9126 quality attributes, using real data from case studies. Evaluation results are compared to other aggregation methods to demonstrate the Choquet integral's ability to model interactions among criteria.
The document discusses movie recommendation systems. It describes how recommendation systems work by predicting a user's rating or preference for an item based on their past ratings and preferences. It outlines several methods used in recommendation systems, including collaborative filtering, content-based filtering, and hybrid systems. It also discusses some specific types of recommendation systems like multi-criteria, risk-aware, and mobile recommender systems. The document provides examples of companies that use recommendation systems and classifications and techniques used to develop these systems.
RANKING BASED ON COLLABORATIVE FEATURE-WEIGHTING APPLIED TO THE RECOMMENDATIO...ijaia
Current research on recommendation systems focuses on optimization and evaluation of the quality
of ranked recommended results. One of the most common approaches used in digital paper
libraries to present and recommend relevant search results, is ranking the papers based on their
features. However, feature utility or relevance varies greatly from highly relevant to less relevant,
and redundant. Departing from the existing recommendation systems, in which all item features
are considered to be equally important, this study presents the initial development of an approach
to feature weighting with the goal of obtaining a novel recommendation method in which features
which are more effective have a higher contribution/weight to the ranking process. Furthermore,
it focuses on obtaining ranking of results returned by a query through a collaborative weighting
procedure carried out by human users. The collaborative feature-weighting procedure is shown to
be incremental, which in turn leads to an incremental approach to feature-based similarity evaluation.
The obtained system is then evaluated using Normalized Discounted Cumulative Gain
(NDCG) with respect to a crowd-sourced ranked results. Comparison between the performance of
the proposed and Ranking SVM methods shows that the overall ranking accuracy of the proposed
approach outperforms the ranking accuracy of Ranking SVM method.
Personalized recommendation for cold start usersIRJET Journal
The document discusses personalized recommendation methods for cold start users. It describes several recommendation techniques including content-based filtering, collaborative filtering, and hybrid recommendation. It also discusses challenges like cold start problems and data sparsity. Trust-based recommendation systems are described that incorporate social relationships between users. Matrix factorization techniques are discussed for modeling user-item interactions and incorporating additional contextual factors. The use of probabilistic matrix factorization models to address cold start and sparsity problems is also covered.
IRJET- Analysis of Rating Difference and User InterestIRJET Journal
This document summarizes a research paper that proposes a collaborative filtering recommendation algorithm that incorporates rating differences and user interests. It first adds a rating difference factor to the traditional collaborative filtering algorithm. It then calculates user interests based on item attributes and the similarity between user interests. Recommendations are made by weighting user rating differences and interest similarities. The proposed algorithm is shown to reduce error rates and improve accuracy compared to traditional collaborative filtering.
The document proposes a framework called TRUE-REPUTATION to calculate trustworthy product reputations from online ratings. It addresses the problem of "false reputations" which can occur when some ratings are intentionally unfair. TRUE-REPUTATION iteratively computes a rating's confidence based on the user's activity, objectivity and consistency, and adjusts the product's reputation accordingly. It determines these factors by analyzing characteristics of reliable information from previous research. The goal is to reduce the impact of unfair ratings while including all ratings to avoid excluding normal users.
This document summarizes several research papers on improving recommendation systems using item-based collaborative filtering approaches. It discusses challenges with traditional collaborative filtering like data sparsity and scalability. It then summarizes various item-based recommendation algorithms that analyze item relationships to indirectly compute recommendations. These include item-item similarity techniques like cosine similarity and adjusting for average ratings. The document also reviews literature on combining item categories and interestingness measures to improve accuracy. Overall, it analyzes different item-based collaborative filtering techniques to address challenges and provide high quality, personalized recommendations at scale.
This document outlines a proposed framework called TKmeans++ for identifying grey sheep users (GSU) and recommending items to them based on trust relations. The framework has two phases: a GSU identification phase that calculates user weights based on similarity, influence, and trust to assign users to clusters, and a recommendation phase that recommends top items to a GSU based on items positively rated by other GSU. An experimental study on the Epinions dataset shows TKmeans++ outperforms other clustering algorithms on MAE and coverage metrics for recommending to GSU. Future work could explore matrix factorization approaches or combining clustering and matrix factorization.
IRJET- Review on Different Recommendation Techniques for GRS in Online Social...IRJET Journal
This document reviews different recommendation techniques for group recommender systems (GRS) in online social networks. It discusses traditional recommender approaches like content-based filtering and collaborative filtering. It also reviews related work applying opinion dynamics models and weight matrices to GRS. The document concludes that using a smart weights matrix to consider relationships between group members' preferences in a recommendation process improves aggregation and ensures consensus, providing the best way to recommend items to a complete group.
Tourism Based Hybrid Recommendation SystemIRJET Journal
This paper proposes a hybrid tourism recommendation system that combines collaborative filtering, content-based filtering, and aspect-based sentiment analysis to improve accuracy and address cold start problems. The system analyzes user ratings and reviews to predict ratings for other tourism packages. It stores ratings, reviews, and sentiment information in a database to enhance recommendations. Results showed the hybrid approach increased efficiency over conventional methods. Future work could include testing on additional datasets and expanding the system.
Similar to A Novel Nonadditive Collaborative-Filtering Approach Using Multicriteria Ratings (20)
Entering College Essay. Top 10 Tips For College AdmissNat Rice
The document summarizes the discovery of a new species, Alborum Plumae, found in Mount Kosciuszko National Park in Australia. Dr. Ella Beard discovered small feathered creatures perfectly camouflaged as snow lumps on tree branches. Early analysis finds they spend most of their time stationary to avoid detection, using their wings only for escaping predators. While sharing traits with birds like down insulation and wing-aided flight, further research is needed to determine their exact taxonomic classification.
006 Essay Example First Paragraph In An ThatsnoNat Rice
The document summarizes racism depicted in two novels by John Updike: Rabbit Run and Rabbit Redux. It notes that both books show racism as an issue, with characters making racist comments about black people. Specific quotes are presented that demonstrate racist language used by characters towards black individuals. The racism portrayed is less extreme in Rabbit Redux compared to Rabbit Run. Overall, the document analyzes how Updike explores themes of racism through his famous character Harry Rabbit and the other characters in these two novels from his Rabbit series.
The document provides instructions for requesting essay writing help from HelpWriting.net in 5 steps:
1) Create an account with a password and email.
2) Complete a 10-minute order form with instructions, sources, and deadline.
3) Choose a bid from writers based on qualifications and feedback.
4) Review the paper and authorize payment or request revisions.
5) Request multiple revisions to ensure satisfaction, with a full refund option for plagiarism.
How To Motivate Yourself To Write An Essay Write EssNat Rice
Here are the key steps to effectively roll out a new leadership philosophy and goals for success across an organization:
1. The CEO should clearly communicate the new philosophy and goals to all levels of management. This includes presenting the vision, values and expected outcomes in all-staff meetings, video conferences, and written updates.
2. Department heads and managers should then cascade the information to their direct reports. One-on-one and team meetings allow for discussion, feedback and alignment around implementation. Training may be required to ensure consistent understanding.
3. Front-line supervisors play a vital role in socializing the changes with their teams on a daily basis. Through leading by example, coaching and regular check-ins, they can reinforce
PPT - Writing The Research Paper PowerPoint Presentation, Free DNat Rice
The document provides instructions for creating an account and submitting a paper writing request on the HelpWriting.net website. It outlines a 5-step process: 1) Create an account with an email and password. 2) Complete a form with paper details, sources, and deadline. 3) Review writer bids and choose one based on qualifications. 4) Review the completed paper and authorize payment. 5) Request revisions until satisfied with the paper. The document promotes HelpWriting.net's writing services and assurances of original, high-quality content.
The document describes a significant event in the author's life where they played in an important basketball game as a 12-year-old, highlighting their preparations like putting on extra deodorant and double knotting their shoelaces. On the day of the game, the author felt intimidated by their much taller competition but was determined to play their best. The author leaves some suspense by not revealing the outcome of the game.
How To Start A Persuasive Essay Introduction - Slide ShareNat Rice
The document provides instructions for creating an account and submitting a request for writing assistance on the HelpWriting.net website. It outlines a 5-step process: 1) Create an account with an email and password. 2) Complete an order form with instructions, sources, and deadline. 3) Review bids from writers and choose one. 4) Review the completed paper and authorize payment. 5) Request revisions until satisfied with the work.
Art Project Proposal Example Awesome How To Write ANat Rice
The document outlines a five step process for requesting an assignment writing service from the website HelpWriting.net, including registering for an account, completing an order form with instructions and deadline, reviewing bids from writers and choosing one, receiving the completed paper for review, and having the option to request revisions until satisfied. The process is described as quick and simple to register, with a bidding system to choose a qualified writer within the requested deadline and guarantees of original, high-quality work or a full refund.
The Importance Of Arts And Humanities Essay.Docx - TNat Rice
The document provides instructions for using the HelpWriting.net service to have papers written. It outlines a 5-step process: 1) Create an account with a password and email. 2) Complete an order form with instructions, sources, and deadline. 3) Review bids from writers and choose one. 4) Review the completed paper and authorize payment. 5) Request revisions until satisfied. It emphasizes that original, high-quality content is guaranteed or a full refund will be provided.
For Some Examples, Check Out Www.EssayC. Online assignment writing service.Nat Rice
Here are a few key points about how language is used for social and cultural communication:
- Language allows people to communicate and interact with one another in social settings. It facilitates the sharing of ideas, information, and experiences within a culture.
- The language we learn is influenced by our culture and environment. Different cultures and communities use language in distinct ways to reflect their norms, values, and traditions.
- Oral language skills developed from an early age lay the foundation for literacy. Storybook reading and rich conversations between teachers and students help expand vocabulary and grammar.
- As students enter school, they bring their home language base - whether standard English or another variety. Teachers should build on students' existing language skills to promote
Write-My-Paper-For-Cheap Write My Paper, Essay, WritingNat Rice
This document provides instructions for submitting a paper writing request to the website HelpWriting.net. It outlines a 5-step process: 1) Create an account with an email and password. 2) Complete a 10-minute order form providing instructions, sources, and deadline. 3) Review bids from writers and select one based on qualifications. 4) Review the completed paper and authorize payment if satisfied. 5) Request revisions until fully satisfied, with a refund offered for plagiarized work. The document promotes HelpWriting.net's writing services and assurances of original, high-quality content.
Printable Template Letter To Santa - Printable TemplatesNat Rice
This document provides instructions for requesting writing assistance from HelpWriting.net. It outlines a 5-step process: 1) Create an account with a password and email. 2) Complete a 10-minute order form providing instructions, sources, and deadline. 3) Review bids from writers and select one based on qualifications. 4) Receive the paper and authorize payment if pleased. 5) Request revisions to ensure satisfaction, with a refund option for plagiarized content.
Essay Websites How To Write And Essay ConclusionNat Rice
The document discusses Boudicca, a Celtic queen who led a major revolt against Roman rule in Britain in AD 61. While the revolt was ultimately a military failure, it was a defining moment in British history that showed resistance to Roman domination. The revolt is primarily known through accounts by Roman historians Cornelius Tacitus and Cassius Dio, who presented the British in a negative light. However, their works remain the most credible primary sources on the events, despite obvious Roman biases.
The document provides instructions for requesting and completing an assignment writing request on the website HelpWriting.net. It outlines a 5-step process: 1) Create an account; 2) Complete an order form with instructions and deadline; 3) Review bids from writers and select one; 4) Review the completed paper and authorize payment; 5) Request revisions to ensure satisfaction. It emphasizes the original, high-quality work and refund policy if plagiarism occurs.
Hugh Gallagher Essay Hugh G. Online assignment writing service.Nat Rice
The document provides instructions for requesting writing assistance on the HelpWriting.net website. It outlines a 5-step process: 1) Create an account with a password and email. 2) Complete a 10-minute order form providing instructions, sources, and deadline. 3) Review bids from writers and choose one based on qualifications. 4) Review the completed paper and authorize payment if satisfied. 5) Request revisions to ensure satisfaction, with the option of a full refund for plagiarized work.
An Essay With A Introduction. Online assignment writing service.Nat Rice
The document discusses the concept of insurgency, which refers to an armed rebellion against a constituted authority. An insurgency can be opposed through counterinsurgency warfare, measures to protect the population, and political/economic actions aimed at undermining the insurgents' claims. Insurgencies exist in an ambiguous legal and conceptual space, as not all rebellions qualify as insurgencies under international law.
How To Write A Philosophical Essay An Ultimate GuideNat Rice
The document provides guidance on writing a philosophical essay and summarizing academic texts. It outlines a 5-step process: 1) create an account, 2) complete an order form with instructions and deadline, 3) review writer bids and choose one, 4) ensure the paper meets expectations and pay the writer, 5) request revisions until satisfied. It also summarizes strategies for solving the Cuban Missile Crisis and analyzing themes in Macbeth related to ambition and self-destruction.
50 Self Evaluation Examples, Forms Questions - Template LabNat Rice
The document discusses the song "Bohemian Rhapsody" by Queen and how it broke conventions. It notes that the song has no chorus and instead has different sections like an intro, ballad, operatic passage, and hard rock section. It describes how the tempo, vocals, instrumentation, and dynamics change throughout the song, making it unique compared to typical song structure. The song brought together different musical textures and styles in a way that was groundbreaking and helped make it one of the greatest songs ever.
40+ Grant Proposal Templates [NSF, Non-ProfiNat Rice
The document discusses performance enhancing drugs in sports and argues they should be legalized. It notes their widespread current use in sports and how testing cannot detect all drug use. It also argues athletes take health risks willingly and fans want to see peak performance, so banning drugs is unreasonable and hypocritical. Legalization with regulation could better protect athlete health while satisfying fan interests.
Nurse Practitioner Essay Family Nurse Practitioner GNat Rice
The document discusses the Flapper and Gibson Girl styles that were popular for women in the late 19th and early 20th centuries. These styles represented different images of the modern woman - Flappers dressed more casually while Gibson Girls emphasized traditional femininity through corsets and accentuating their figures. Both styles nonetheless promoted women's rights and equality as women took on new social roles during this period.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
2. 2 Mathematical Problems in Engineering
These recommendation systems do not allow users to specify
their subjective perception of the various criteria of individ-
ual items.
From the viewpoint of multicriteria decision making
(MCDM), the overall rating has a certain relationship with
the multicriteria ratings for an item. For this, in contrast
to the multicriteria recommendation systems previously
described, Adomavicius and Kwon [5] presented a frame-
work for an aggregation-function-based approach to leverage
multicriteria rating information, in which the rating for each
criterion can be estimated by the traditional similarity-based
approach using single-criterion ratings. Then the output of
an aggregation function is regarded as a predicted value of
the overall rating of an unrated item. The weighted average
method (WAM) is often used as an aggregation function and
can aggregate ratings on different criteria when the criterion
weights are available [5, 10]. Note that the criterion weights in
WAM are interpreted as the relative importance of the crite-
ria. The WAM is a simple decomposed method and assumes
that criteria do not interact [11]. However, because the criteria
are not always independent, the assumption of additivity is
not always reasonable [12] and may affect recommendation
performance. Thus, this motivates us to use a nonadditive
technique, the Choquet integral [13–16], as an aggregation
function. Actually, the Choquet integral is a generalization
of the weighted average [17, 18]. To address this, this paper
further proposes a novel nonadditive multicriteria recom-
mendation method on the basis of the Choquet integral.
Furthermore, because the goal of the proposed approach is to
recommend correctly a set of a few relevant items to each user,
a variation of the popular 𝐹-measure is presented to evaluate
recommendation performance. To achieve high accuracy, a
genetic algorithm (GA) is implemented to determine the
parameter specifications.
The remainder of the paper is organized as follows.
Section 2 briefly introduces several collaborative-filtering
approaches using multicriteria ratings, including the
similarity-based and the aggregation-function-based
approaches. Section 3 describes the proposed aggregation-
function-based collaborative-filtering approach using the
Choquet integral and presents an accuracy metric for
recommendation performance evaluation. A GA-based
method for constructing a nonadditive recommendation
model is demonstrated in Section 4. Section 5 applies the
proposed nonadditive approach to initiator recommendation
on a group-buying website in Taiwan. Section 6 contains the
discussion and conclusions.
2. Collaborative-Filtering Approaches Using
Multicriteria Ratings
Collaborative-filtering approaches rely on the ratings of a
user as well as those of other users in the system [19]. The
key idea is to recommend items that users with similar
preferences have liked in the past. Traditional collaborative-
filtering approaches using single-criterion rating can be cat-
egorized into two classes: neighborhood-based and model-
based approaches. Adomavicius and Kwon [5] presented
the similarity-based and aggregation-function-based meth-
ods within neighborhood-based approaches. The latter is the
focus of this paper.
2.1. Similarity-Based Approach. Assume that a system asks
each user to offer feedback on 𝑛 criteria with respect to a
consumed item or a person with whom he or she has a
connection. Let 𝑅0 denote the set of possible overall ratings,
and let 𝑅𝑖 denote the set of possible ratings for each individual
criterion (1 ≤ 𝑖 ≤ 𝑛). For the (user, item) pairs, the rating
function 𝑅 in a multicriteria recommender system is defined
as follows:
𝑅 (user, item) → 𝑅0 × 𝑅1 × ⋅ ⋅ ⋅ × 𝑅𝑛. (1)
For instance, for simplicity only the reputation (criterion 1)
and the response (criterion 2) are used to evaluate an initiator
on a group-buying website (i.e., 𝑛 = 2) for the initiator
recommendation. User Randy might assign ratings of 5, 7,
and 6 to the reputation, the response, and the overall rating,
respectively, for initiator Ryan. Of course, it is necessary
that Randy has already joined the group confirmed by Ryan.
Therefore, 𝑅(Randy, Ryan) can be denoted by (𝑟
Randy, Ryan
0 ,
𝑟
Randy, Ryan
1 , 𝑟
Randy, Ryan
2 ) = (6, 5, 7). If user Frances has not
yet joined the group confirmed by Ryan, the recommender
system would directly estimate the overall rating that Frances
would give to Ryan (i.e., 𝑟
Frances,Ryan
0 ) by estimating 𝑅.
In this example, without losing generality, the estimate of
the overall rating that Frances would give to Ryan is based
on the similarity between Frances and user 𝑢, denoted by
sim(Frances, 𝑢), who rated Ryan; meanwhile, the similarity
is calculated according to the initiators that Frances and user
𝑢 have both rated previously. The more similar Frances and 𝑢
are, the more 𝑟
𝑢, Ryan
0 would contribute to 𝑟
Frances, Ryan
0 .
The cosine-based similarity measure is most commonly
used to derive sim𝑖(Frances, 𝑢) on criterion 𝑖. sim𝑖(Frances, 𝑢)
is defined as
sim𝑖 (Frances, 𝑢) = ( ∑
𝑗∈𝐼(Frances, 𝑢)
𝑟
Frances, 𝑗
𝑖 𝑟
𝑢, 𝑗
𝑖 )
× (√ ∑
𝑗∈𝐼(Frances, 𝑢)
(𝑟
Frances, 𝑗
𝑖 )
2
× √ ∑
𝑗∈𝐼(Frances, 𝑢)
(𝑟
𝑢, 𝑗
𝑖 )
2
)
−1
,
= 1, . . . , 𝑛,
(2)
where 𝐼(Frances, 𝑢) represents the sets of initiators rated by
both Frances and user 𝑢. sim(Frances, 𝑢) is a used-based
average obtained by aggregating the individual similarities in
several ways as follows:
(1) average similarity:
sim (Frances, 𝑢) =
1
𝑛 + 1
𝑛
∑
𝑖=0
sim𝑖 (Frances, 𝑢) ; (3)
3. Mathematical Problems in Engineering 3
(2) worst-case similarity:
sim (Frances, 𝑢) = min
𝑖=0,...,𝑛
sim𝑖 (Frances, 𝑢) . (4)
In addition to the cosine-based similarity measure, a
distance-based similarity can be formulated as follows:
sim (Frances, 𝑢)
= 1 × (1 +
1
|𝐼 (Frances, 𝑢)|
× ∑
𝑗∈𝐼(Frances, 𝑢)
𝑑 (𝑅 (Frances, 𝑗) , 𝑅 (𝑢, 𝑗)))
−1
,
(5)
where 𝑑(𝑅(Frances, 𝑗), 𝑅(𝑢, 𝑗)) can be derived by various
distance metrics, for example,
(i) Manhattan distance:
𝑑 (𝑅 (Frances, 𝑗) , 𝑅 (𝑢, 𝑗)) =
𝑛+1
∑
𝑖=0
𝑟
Frances, 𝑗
𝑖 − 𝑟
𝑢, 𝑗
𝑖
; (6)
(ii) Euclidean distance:
𝑑 (𝑅 (Frances, 𝑗) , 𝑅 (𝑢, 𝑗)) = √
𝑛+1
∑
𝑖=0
(𝑟
Frances,𝑗
𝑖 − 𝑟
𝑢, 𝑗
𝑖 )
2
; (7)
(iii) Chebyshev distance:
𝑑 (𝑅 (Frances, 𝑗) , 𝑅 (𝑢, 𝑗)) = max
𝑖=0,..., 𝑛
𝑟
Frances,𝑗
𝑖 − 𝑟
𝑢, 𝑗
𝑖
. (8)
The predicted overall rating 𝑟
Frances, Ryan
0 can then be defined
by a weighted average of 𝑟
𝑢, Ryan
0 :
𝑟
Frances, Ryan
0 = 𝑒(Frances)
+
∑𝑢 sim (Frances, 𝑢) (𝑟
𝑢, Ryan
0 − 𝑒(𝑢))
∑𝑢 sim (Frances, 𝑢)
,
(9)
where 𝑒(𝑢) represents the average overall rating of user 𝑢. This
formulation has been used by the well-known GroupLens
[20] to provide personalized predictions for Usenet news [21].
As for the single-criterion rating systems, the rating
function 𝑅 for the (user, item) pairs is defined as follows:
𝑅 (user, item) → 𝑅0, (10)
where sim(Frances, 𝑢) is simply specified as sim0(Frances, 𝑢)
to obtain 𝑟
Frances, Ryan
0 .
2.2. Aggregation-Function-Based Approach. In contrast to the
similarity-based approach, the aggregation-function-based
approach assumes that a certain relationship exists between
the overall rating and the multicriteria ratings of items.
Undoubtedly, the aggregation function plays an important
role for an aggregation-function-based approach. The rating
function 𝑅 is defined as follows:
𝑅 (user, item) → 𝑅𝑖, 𝑖 = 1, . . . , 𝑛. (11)
Following the example in the previous subsection, instead of
computing the individual similarity weights, it is necessary
to estimate that ratings of the reputation (i.e., 𝑟
Frances, Ryan
1 )
and the response (i.e., 𝑟
Frances, Ryan
2 ) that Frances would give to
Ryan can be estimated by a user-based deviation-from-mean
method as follows:
𝑟
Frances, Ryan
𝑖 = 𝑒𝑖(Frances)
+
∑𝑢 sim𝑖 (Frances, 𝑢) (𝑟
𝑢, Ryan
𝑖 − 𝑒𝑖 (𝑢))
∑𝑢 sim𝑖 (Frances, 𝑢)
,
𝑖 = 1, 2,
(12)
where 𝑒𝑖(𝑢) represents the average overall rating of user 𝑢
for criterion 𝑖. 𝑟
Frances, Ryan
𝑖 can be obtained by considering the
cosine-based similarity measure. Then 𝑟
Frances, Ryan
0 is further
predicted by aggregating 𝑟
Frances, Ryan
1 and 𝑟
Frances, Ryan
2 . There-
fore, the focus of the similarity-based and the aggregation-
function-based approaches is quite different. The WAM is
often used to aggregate the partial ratings (i.e., 𝑟
Frances, Ryan
1 and
𝑟
Frances, Ryan
2 ) when 𝑤1 and 𝑤2 have been assigned:
𝑟
Frances, Ryan
0 = 𝑤1𝑟
Frances, Ryan
1 + 𝑤2𝑟
Frances, Ryan
2 , (13)
where 𝑤1 + 𝑤2 = 1. This means that a classical set
function 𝜇 can be defined on {𝑟
Frances, Ryan
1 , 𝑟
Frances, Ryan
2 }
with 𝜇(𝑟
Frances, Ryan
1 ) = 𝑤1 and 𝜇(𝑟
Frances, Ryan
2 ) = 𝑤2
such that 𝜇({𝑟
Frances, Ryan
1 , 𝑟
Frances, Ryan
2 }) = 𝜇(𝑟
Frances, Ryan
1 ) +
𝜇(𝑟
Frances, Ryan
2 ). The additivity of 𝜇 indicates that there exists
no interactions among 𝑟
Frances, Ryan
1 and 𝑟
Frances, Ryan
2 . Unfortu-
nately, as mentioned above, this assumption is not warranted
in many applications [4]. Because the fuzzy integral does not
assume the independence of elements [17, 18], it is reasonable
to obtain 𝑟
Frances, Ryan
0 by using a nonadditive Choquet integral
to aggregate 𝑟
Frances, Ryan
1 and 𝑟
Frances, Ryan
2 .
3. Non-Additive Aggregation-Function-Based
Collaborative-Filtering Approach
In this section, the fuzzy measure used for describing the
interaction among attributes in a set is first described in
Section 3.1. Section 3.2 presents the proposed approach using
the Choquet integral and an accuracy metric for recommen-
dation performance evaluation.
4. 4 Mathematical Problems in Engineering
3.1. Description of the Interaction Using a Fuzzy Measure. Let
𝑃(𝑋) denote the power set of 𝑋 = {𝑥1, 𝑥2, . . . , 𝑥𝑛}, where 𝑋 is
called the feature space. Then (𝑋, 𝑃(𝑋)) is a measurable space.
A nonadditive and nonnegative set function 𝜇 : 𝑃(𝑋) →
[0, 1] is a fuzzy measure that satisfies the following conditions
[22–24]:
(1) 𝜇(Ø) = 0;
(2) for all 𝑅, 𝑆 ∈ 𝑃(𝑋), if 𝑅 ⊂ 𝑆, then 𝜇(𝑅) ≤ 𝜇(𝑆)
(monotonicity);
(3) for every sequence of subsets of 𝑋, if either 𝑅1 ⊆
𝑅2 ⊆ ⋅ ⋅ ⋅ or 𝑅1 ⊇ 𝑅2 ⊇ ⋅ ⋅ ⋅ , then lim𝑖 → ∞𝜇(𝑅𝑖) =
𝜇(lim𝑖 → ∞𝑅𝑖) (continuity).
When 𝜇(𝑋) = 1, 𝜇 is said to be regular. The fuzzy measure
is developed to consider the interaction among attributes
towards the objective attribute [17] by replacing the usual
additive property with the monotonic property.
Let 𝜇𝑘 denote 𝜇({𝑥𝑘}), which is called a fuzzy density, and
𝐸𝑘 = {𝑥𝑘, 𝑥𝑘+1, . . . , 𝑥𝑛} (1 ≤ 𝑘 ≤ 𝑛), where 0 ≤ 𝜇𝑘 ≤
1. Interaction among the attributes of 𝐸𝑘 can be described
using 𝜇(𝐸𝑘), which expresses the relative importance or
discriminatory power of 𝐸𝑘. This means that 𝜇 can be
regarded as an importance measure and then 𝜇𝑘 can be
interpreted as the degree of importance of 𝑥𝑘. 𝜇(𝐸𝑘) may be
less than or greater than 𝜇𝑘 +𝜇𝑘+1 +⋅ ⋅ ⋅+𝜇𝑛, thereby expressing
an interaction among the elements 𝑥𝑘, 𝑥𝑘+1, . . . , 𝑥𝑛 [12]. For
instance, if 𝜇1 = 0.3, 𝜇2 = 0.5, and 𝜇({𝑥1, 𝑥2}) = 0.9, then
𝜇({𝑥1, 𝑥2}) > 𝜇1 + 𝜇2 indicates that the joint contribution of
𝑥1 and 𝑥2 to the decision or the objective attribute is greater
than the sum of their individual contributions. This indicates
that they would enhance each other.
Among the various options for 𝜇, a 𝜆-fuzzy measure is a
convenient means of computing the fuzzy integral [12, 23, 25].
For all 𝑅, 𝑆 ∈ 𝑃(𝑋) with 𝑅 ∩ 𝑆 = Ø, 𝜇 is a 𝜆-fuzzy measure if
it satisfies the following property:
(1)
𝜇 (Ø) = 0, 𝜇 (𝑋) = 1; (14)
(2)
𝜇 (𝑅 ∪ 𝑆) = 𝜇 (𝑅) + 𝜇 (𝑆) + 𝜆𝜇 (𝑅) 𝜇 (𝑆) , 𝜆 ∈ (−1, ∞) .
(15)
The advantage of using the 𝜆-fuzzy measure is that, after
determining the fuzzy densities 𝜇1, 𝜇2, . . . , 𝜇𝑛, 𝜆 can be
uniquely determined from the condition 𝜇(𝑋) = 1. 𝜇(𝐸𝑘) can
be further determined by 𝜆 and 𝜇𝑗 as follows:
𝜇 (𝐸𝑘) =
1
𝜆
[ ∏
𝑖=𝑘⋅⋅⋅𝑛
(1 + 𝜆𝜇𝑖) − 1] . (16)
As mentioned above, 𝜇(𝑅 ∪ 𝑆) expresses the importance of
𝑅 ∪ 𝑆. The value of 𝜆 determines the nature of the interaction
between 𝑅 and 𝑆. If 𝜆 > 0, there is a multiplicative effect
between 𝑅 and 𝑆 (i.e., 𝑅 and 𝑆 are superadditive); if 𝜆 < 0
there is a substitutive effect between 𝑅 and 𝑆 (i.e., 𝑅 and 𝑆
are subadditive). If 𝜆 = 0, then 𝑅 and 𝑆 are not interactive:
𝜇(𝑅∪𝑆) = 𝜇(𝑅)+𝜇(𝑆). Actually, the sign of 𝜆 can be identified
by ∑𝑛
𝑖=1 𝜇𝑖. In other words, if ∑𝑛
𝑖=1 𝜇𝑖 > 1, then −1 < 𝜆 < 0; if
∑𝑛
𝑖=1 𝜇𝑖 < 1, then 𝜆 > 0; and if ∑𝑛
𝑖=1 𝜇𝑖 = 1, then 𝜆 = 0.
𝜇(En) 𝜇(En−1) · · ·
.
.
𝜇(E2) 𝜇(E1)
f(i)
(Xn)
f(i)
(Xn−1)
f(i)
(X2)
f(i)
(X1)
Figure 1: Graphical representation of Choquet fuzzy integral.
3.2. The Proposed Non-Additive Approach
3.2.1. Aggregating Multicriteria Ratings Using the Choquet
Integral. To consider interactions among criteria, a nonaddi-
tive collaborative-filtering approach is proposed to estimate,
for instance, 𝑟𝑢, V
0 , using the Choquet integral, where V is
an initiator but has not been rated by 𝑢. The Choquet
integral, which is a generalization of the linear Lebesgue
integral (e.g., the weighted average method) [17], can be
represented in terms of fuzzy measures [12, 18]. Let x𝑖 =
(𝑥𝑖1, 𝑥𝑖2, . . . , 𝑥𝑖𝑛) = (𝑟𝑢, V
1 , 𝑟𝑢, V
2 , . . . , 𝑟𝑢, V
𝑛 ). For the proposed
nonadditive aggregation-function-based approach, the syn-
thetic evaluation of x𝑖 can be further obtained by the Choquet
integral. Let 𝑓(𝑖)
with respect to x𝑖 be a non-negative, real-
valued measurable function defined on 𝑋 such that 𝑓(𝑖)
(𝑥𝑘) =
𝑥𝑖𝑘 (𝑘 = 1, 2, . . . , 𝑛) falls into a certain range. The element
in 𝑋 with min{𝑓(𝑖)
(𝑥𝑘) | 𝑘 = 1, 2, . . . , 𝑛} is renumbered as
one, where 𝑓(𝑖)
(𝑥𝑘) denotes the performance or observation
value of 𝑥𝑘 with respect to x𝑖. In other words, all elements
𝑥𝑘 are rearranged in order of descending 𝑓(𝑖)
(𝑥𝑘), so that
𝑓(𝑖)
(𝑥1) ≤ 𝑓(𝑖)
(𝑥2) ≤ ⋅ ⋅ ⋅ ≤ 𝑓(𝑖)
(𝑥𝑛). As illustrated in Figure 1,
the Choquet integral (𝑐) ∫ 𝑓(𝑖)
d𝜇 over 𝑋 of 𝑓 with respect to
𝜇 is defined as follows:
(𝑐) ∫ 𝑓(𝑖)
d𝜇 =
𝑛
∑
𝑘=1
𝑓(𝑖)
(𝑥𝑘) (𝜇 (𝐸𝑘) − 𝜇 (𝐸𝑘+1)) , (17)
where 𝜇(𝐸𝑛+1) is specified as zero and 𝑅0(𝑢, V) = (𝑐) ∫ 𝑓(𝑖)
d𝜇.
If ∑𝑗 𝜇𝑗 is equal to one, the Choquet integral coincides with
the WAM.
3.2.2. Evaluating Recommendation Performance. The perfor-
mance of a recommendation approach can be evaluated by
decision-support accuracy metrics which determine how well
the recommendation approach can predict items the user
would rate highly. Commonly used metrics are precision,
recall, and the 𝐹-measure. Precision is the number of truly
high overall ratings expressed as a fraction of the total
number of ratings that the system predicted they would be
high; recall is the number of correctly predicted high ratings
expressed as a fraction of all the ratings known to be high,
while the 𝐹-measure is the harmonic mean of precision
and recall. Often, there is an inverse relationship between
precision and recall because it is possible to increase one at
5. Mathematical Problems in Engineering 5
the cost of reducing the other. Usually, precision and recall
scores are not discussed in isolation. Therefore, it pays to take
into account the 𝐹-measure [1] as follows:
𝐹 =
2precision ⋅ recall
precision + recall
, (18)
where recall and precision are evenly weighted. However, the
actual weights on precision and recall should be dependent
on the goal of a recommendation approach. van Rijsbergen
[26] further proposed the 𝐹𝛽 measure as follows:
𝐹𝛽 = (1 + 𝛽2
)
precision ⋅ recall
𝛽2precision + recall
, (19)
where 𝛽 ≥ 0. 𝐹𝛽 weights recall higher than precision when
𝛽 > 1 and weights precision higher than recall when 𝛽 < 1.
Clearly, the original 𝐹-measure is simply the 𝐹1 measure.
From the viewpoint of practicality, many users of recom-
mendation applications are typically interested in only the
few highest-ranked item recommendations [5]. Therefore,
the popular metric related to precision, namely, precision-in-
top-𝑁 (𝑁 = 1, 2, 3, . . .), should be taken into account for the
proposed method. This metric is defined as the fraction of
truly high overall ratings among those the system predicted
would be the 𝑁 relevant items for each user. Furthermore, it
is reasonable to place more emphasis on precision than on
recall, to highlight the significance of precision for users. For
this, a variation of the 𝐹𝛽 measure that places emphasis on
precision-in-top-𝑁 is presented to evaluate the performance
of the proposed nonadditive recommendation approach:
V𝐹𝛽 = (1 + 𝛽2
)
precision-in-top-𝑁 ⋅ recall
𝛽2precision-in-top-𝑁 + recall
, (20)
where 0 ≤ 𝛽 ≤ 1.
4. A GA-Based Method for Constructing a
Non-Additive Recommendation Model
4.1. Constructing a Non-Additive Recommendation Model
Using Multicriteria Ratings. The proposed model does not
involve any complicated mechanisms for selecting the free
parameters. Because decision-makers cannot easily pre-
specify the criterion weights, a real-valued GA-based method
is used here, involving the basic operations of selection,
crossover, and mutation [27, 28] to determine the optimal
values of the criterion weights (i.e., 𝜇1, 𝜇2, . . . , 𝜇𝑛). Let 𝑛size
and 𝑛max denote the population size and the total number
of generations, respectively. The following steps are used
to construct a recommendation model using the proposed
nonadditive collaborative-filtering approach.
Algorithm 1. Construct a nonadditive recommendation
model using the collaborative-filtering approach.
Input. Population size (𝑁pop); stopping condition (𝑁con, i.e.,
total number of generations); number of elite chromosomes
(𝑁del); crossover probability (Pr𝑐); mutation probability
(Pr𝑚); the value of 𝛽 for V𝐹𝛽 measure; the value of 𝑁 for the
precision-in-top-𝑁 measure; a set of training patterns.
Output. A nonadditive recommendation model using the
collaborative-filtering approach with a higher V𝐹𝛽 measure.
Method
Step 1. Population Initialization. Generate an initial popula-
tion of 𝑛size chromosomes, each consisting of 𝑛 real-valued
parameters. Randomly assign a real value chosen from the
interval [0, 1] to each parameter in a chromosome.
Step 2. Chromosome Evaluation. Compute the fitness value for
each chromosome. Because the objective of the algorithm is
to construct a nonadditive recommendation model using the
collaborative-filtering approach with a higher V𝐹𝛽 measure,
the V𝐹𝛽 measure is used as the fitness function for evaluating
a chromosome.
Step 3. Generation of New Chromosomes. Generate a new
generation of 𝑛size chromosomes by selection, crossover, and
mutation.
Step 4. Elitist Strategy. Randomly remove 𝑛del (0 ≤ 𝑛del ≤
𝑛size) of the newly generated chromosomes. Insert 𝑛del copies
of the chromosome with maximum fitness in the previous
generation.
Step 5. Termination Test. Terminate the algorithm if 𝑛max
generations have been generated; otherwise, return to Step 2.
When the stopping condition is satisfied, the algorithm
is terminated and whichever chromosome has the maximum
fitness among all generations serves as the desired solution.
It is noted that the above algorithm can also be applied
to construct an additive recommendation model using the
WAM.
4.2. Genetic Operations. Let 𝑃𝑘 denote the population gener-
ated in generation 𝑘 (1 ≤ 𝑘 ≤ 𝑛max). Chromosome 𝑖 (1 ≤
𝑘 ≤ 𝑛size) generated in 𝑃𝑘 is represented by 𝜇𝑘
𝑖1 𝜇𝑘
𝑖2 ⋅ ⋅ ⋅ 𝜇𝑘
𝑖𝑛.
After evaluating the fitness value for each chromosome
in 𝑃𝑘, selection, crossover, and mutation are applied until
𝑛size new chromosomes have been generated for 𝑃𝑘+1. These
genetic operations are described in more detail below. In
contrast to a nonadditive recommendation model, for an
additive recommendation model using the WAM, 𝜇𝑘
𝑖𝑗 can be
specifically set as follows before evaluating the fitness value:
𝜇𝑘
𝑖𝑗 =
𝜇𝑘
𝑖𝑗
𝜁
, (21)
where 𝜁 = 𝜇𝑘
𝑖1 + 𝜇𝑘
𝑖2 + ⋅ ⋅ ⋅ + 𝜇𝑘
𝑖𝑛.
4.2.1. Selection. Using the binary tournament selection, two
chromosomes from the current population are randomly
selected, and the one with the higher fitness is placed in a
mating pool. This process is repeated until there are 𝑛size
chromosomes in the mating pool. Next, 𝑛size pairs of chro-
mosomes from the pool are randomly selected for mating.
6. 6 Mathematical Problems in Engineering
The crossover and mutation operations are applied to the
parents to generate children.
4.2.2. Crossover. For each mated pair of chromosomes 𝑖 and
𝑗, 𝜇𝑘
𝑖1 𝜇𝑘
𝑖2 ⋅ ⋅ ⋅ 𝜇𝑘
𝑖𝑛 and 𝜇𝑘
𝑗1 𝜇𝑘
𝑗2 ⋅ ⋅ ⋅ 𝜇𝑘
𝑗𝑛, each pair of genes has a
probability Pr𝑐 of undergoing the crossover operation. The
operations are performed as 𝜇𝑘
𝑖𝑤
= 𝑎𝑤𝜇𝑘
𝑖𝑤 + (1 − 𝑎𝑤)𝜇𝑘
𝑗𝑤,
𝜇𝑘
𝑗𝑤
= (1 − 𝑎𝑤)𝜇𝑘
𝑖𝑤 + 𝑎𝑤𝜇𝑘
𝑗𝑤 (1 ≤ 𝑤 ≤ 𝑛), where 𝑎𝑤 is a
random number in the interval [0, 1]. Two new chromosomes
are thereby generated, which will replace their parents in
generation 𝑃𝑘+1.
4.2.3. Mutation. There is a probability Pr𝑚 that the mutation
operation will be performed on each real-valued parameter in
new chromosomes generated by the crossover operation. To
avoid excessive perturbation of the gene pool, a low mutation
rate is used. If a mutation occurs for a gene, it will be changed
by adding a number randomly selected from a specified
interval. After crossover and mutation, 𝑛del (0 ≤ 𝑛del ≤ 𝑛size)
chromosomes in 𝑃𝑘+1 are randomly removed from the set of
new chromosomes (those formed by genetic operations) to
make room for additional copies of the chromosome with
maximum fitness value in 𝑃𝑘.
5. Application to Initiator Recommendation
on a Group-Buying Website
Group-buying websites play the role of a transaction platform
between businesses and consumers. The websites call a group
of consumers with the same needs for the purchase of
items and then negotiate with vendors to obtain the best
price or to get a special discount. Groupon, which has the
high market share, is a representative group-buying website.
With group-buying activities increasing and their associated
websites expanding rapidly, a market research institute in
Virginia, BIA/Kelsey, predicted that the group-buying market
in the United States will reach US$ 39.3 billion in 2015
[29]. Undoubtedly, group-buying has become an important
transaction model for online shopping.
In Taiwan, the Institute for Information Industry (MIC)
of Taiwan reported that the group-buying market reached
approximately US$ 2.39 billion in 2010 and is expected
to reach US$ 3 billion by 2011 [30]. In the application,
the proposed recommendation approach has been applied
to initiator recommendation on one popular group-buying
website in Taiwan. Its sales volume was over US$ 0.17 billion
in 2010. On this website, users often search for appropriate
initiators who can bargain with vendors over the price for
certain items. However, due to the large number of search
results, users have suffered from the problem of information
overload, especially for hot items. Furthermore, application
domains in previous research do not involve the initiator
recommendations for the group-buying. This motivates us to
apply the recommendation techniques to this website.
The computer simulations were programmed in Delphi
7.0 and executed on a 2 GHz dual-CPU Pentium computer.
Section 5.1 describes the data collected. Section 5.2 describes
the parameter specification of the GA for the computer
simulations. In Section 5.3, the performance of the proposed
nonadditive recommendation approach is compared with
several recommendation approaches using multicriteria rat-
ings.
5.1. Data Description. A total of 211 undergraduates with
business administration as their major subject and who were
familiar with group-buying participated in the experiment.
Each subject was asked to rate twenty experienced initiators
selected from the above-mentioned website. Each subject
assigned an overall rating and five criterion ratings, namely,
ability, reputation, responsiveness, trust, and interaction, to
each initiator. These criteria are described below.
Ability. This represents knowledge and techniques that can
be used to solve problems for customers [31]. Initiators are
expected not only to have the experience in confirming
groups, but also to solve any problems that arise in group-
buying.
Reputation. This indicates whether the initiators have the
ability and intention to fulfill their promises [32].
Responsiveness. In a virtual community, members always
expect to receive responses to their posted information
from other members [33]. In the group-buying context, this
can promote the establishment of trust among initiators
and group members. Responsiveness indicates whether the
initiators tried to respond to any problems reported by the
group members.
Trust. Based on the viewpoint of trust in [34], it is considered
that the initiators are expected to have a positive expectation
of the intention.
Interaction. Regular communication between sellers and
buyers is helpful in building up the trust of buyers in sellers
[35]. Therefore, initiators are expected to discuss progress
and problems actively with group members during a group-
buying session.
All ratings range from zero, representing “very unsatis-
factory,” to ten, representing “very satisfactory.” The overall
rating indicates how much a user appreciates the initiator.
Because the decision-support measures are used to estimate
accuracy, it is necessary to define every overall rating on a
binary scale [21] as “high-ranked” or “not high-ranked”. It
should be reasonable to translate these overall ratings into
a binary scale by treating the ratings greater than or equal
to seven as high-ranked and those less than seven as not
high-ranked. In other words, the initiators whose ratings are
greater than or equal to seven are relevant to the users.
The leave-ten-out technique is used to examine the
generalization ability of different recommendation. In each of
the iterations, ten evaluations given by a subject are randomly
selected to serve as test data, and the remaining evaluations
were chosen as the training data. This means that test data
are produced for each subject in each of the iterations. Then
the overall rating was predicted for each evaluation in the
test data based on the information in the training data. The
precision-in-top-𝑁 for the test data can also be obtained.
7. Mathematical Problems in Engineering 7
Table 1: V𝐹𝛽 of different methods.
Classification method
𝛽
1 1/2 1/3 1/4 1/5 1/6 1/7 1/8
Single-criterion rating 0.545 0.676 0.735 0.762 0.776 0.784 0.789 0.793
Average similarity 0.546 0.681 0.742 0.770 0.785 0.794 0.799 0.803
Worst-case similarity 0.536 0.671 0.733 0.762 0.777 0.785 0.791 0.795
Manhattan distance 0.563 0.707 0.773 0.803 0.820 0.829 0.835 0.839
Euclidean distance 0.553 0.691 0.753 0.782 0.797 0.806 0.812 0.815
Chebyshev distance 0.553 0.688 0.749 0.777 0.792 0.801 0.806 0.810
WAM 0.569 0.682 0.735 0.756 0.769 0.793 0.789 0.792
Non-additive approach 0.657 0.719 0.751 0.779 0.797 0.822 0.837 0.851
This procedure is iterated until the evaluations of each of the
subjects have been used as the test data. Because the results
of a random sampling procedure may be dependent on the
selection of evaluations, the above procedure is repeated five
times.
5.2. GA Parameter Specifications. A number of factors can
influence GA performance, including the size of the pop-
ulation and the probabilities of applying the crossover and
mutation operators. Unfortunately, there is no standard
procedure for choosing optimal GA specifications. Based on
the principles suggested by Osyczka [36] and Ishibuchi et al.
[37], the parameters are specified as follows:
(i) 𝑛size = 50: GA populations commonly range from
50 to 500 individuals. Hence, 50 individuals is an
acceptable size;
(ii) 𝑛max = 500: the stopping condition is specified
according to the available computing time;
(iii) 𝑛del = 2: only a small number of elite chromosomes
are used;
(iv) Pr𝑐 = 1.0, Pr𝑚 = 0.01: since Pr𝑐 controls the range of
exploration in the solution space, most sources rec-
ommend choosing a large value. To avoid generating
an excessive perturbation Pr𝑚 should be set to a small
value;
(v) 𝑁 = 5: it is assumed that users required the system
to recommend the five most highly ranked initiators.
In other words, the precision-in-top-5 is incorporated
into the V𝐹𝛽 measure;
(vi) 𝛽 is specified as 1, 1/2, 1/3, . . . , 1/8. A recommender
system is constructed for each 𝛽 value.
Although the above specifications are somewhat subjective,
the experimental results show that they are acceptable.
Therefore, customized parameter tuning is not considered for
the proposed approach.
5.3. Performance Evaluation. The proposed nonadditive
approach is compared with several collaborative-filtering
approaches introduced in the previous section: the traditional
single-criterion rating approach, similarity-based approaches
using multicriteria ratings with average similarity, worst-case
similarity, distance-based similarity as described in [5], and
an aggregation-function-based approach using the WAM. By
a random sampling procedure with 50% training data and
50% test data, the average results of these approaches are
obtained from five trials. For each evaluation in the test data,
the evaluated initiator is treated as the target item. Each
approach considered is used to predict the overall rating
that the target item would have by using the training data.
Then, “high-ranked” or “not high-ranked” for each target
item could be determined by its predicted overall rating.
By maximizing V𝐹𝛽 with the precision-in-top-5 measure
for a certain 𝛽, it is interesting to examine the precision-
in-top-1 and precision-in-top-3 for the proposed approach.
The idea is to identify 𝛽 for which the proposed method can
perform well compared with the similarity-based methods
considered for V𝐹𝛽 and various precision-in-top-𝑁 measures
(𝑁 = 1, 3, 5). Table 1 shows that the V𝐹𝛽 value of all the
methods improved from 𝛽 = 1 to 𝛽 = 1/8. This is
reasonable because V𝐹𝛽 approaches precision-in-top-𝑁 when
𝛽 is sufficiently small. The notable results in Tables 1, 2, and 3
can be summarized as follows.
(1) An approach with a higher precision-in-top-5 mea-
sure is not guaranteed to have a higher V𝐹𝛽. For
instance, for 𝛽 = 1 and 1/2; although the V𝐹𝛽
value of the proposed nonadditive approach exceeds
the similarity-based approaches considered, it can be
seen in Table 2 that the precision-in-top-5 measures
obtained by the proposed approach are inferior to
those obtained by the similarity-based approaches
and the WAM.
(2) When 𝛽 ≤ 1/5, the proposed nonadditive approach
performs well compared with the similarity-based
methods using the average similarity and the worst-
case similarity for V𝐹𝛽 and different precision-in-top-
𝑁 measures (𝑁 = 1, 3, 5).
(3) When 𝛽 ≤ 1/7, the proposed nonadditive approach
performs well compared with similarity-based meth-
ods using distance-based similarities for V𝐹𝛽, the
precision-in-top-3 measure, and the precision-in-
top-5 measure.
(4) The proposed nonadditive approach is inferior to
the approaches using distance-based similarities for
8. 8 Mathematical Problems in Engineering
Table 2: Various precisions (%) of different methods.
Method Precision-in-top-1 Precision-in-top-3 Precision-in-top-5
Single-criterion rating 82.02 82.90 80.45
Average similarity 83.02 83.35 81.48
Worst-case similarity 83.52 83.57 80.81
Manhattan distance 93.71 88.55 85.22
Euclidean distance 91.51 86.44 82.77
Chebyshev distance 89.28 85.36 82.17
the precision-in-top-1 measure (i.e., Manhattan and
Euclidean distances) regardless of the value of 𝛽.
(5) When 𝛽 ≤ 1/5, the proposed nonadditive approach
performs well compared with the single-criterion
rating approach for V𝐹𝛽 and various precision-in-top-
𝑁 measures (𝑁 = 1, 3, 5).
(6) The proposed nonadditive approach outperforms the
WAM for V𝐹𝛽 and various precision-in-top-𝑁 mea-
sures (𝑁 = 1, 3, 5) when 𝛽 ≤ 1/4.
(7) Among the similarity-based approaches, the single-
criterion rating approach seems to perform worst for
V𝐹𝛽 and various precision-in-top-𝑁 measures (𝑁 =
1, 3, 5) regardless of the value of 𝛽.
(8) The WAM outperforms the single-criterion rating
approach for the precision-in-top-5 measure when
𝛽 ≤ 1/3. The precision-in-top-1 and precision-in-top-
3 measures of the WAM are inferior to those of the
single-criterion rating approach.
Therefore, by incorporating the precision-in-top-5 measure
into the fitness function (i.e., V𝐹𝛽) with appropriate 𝛽 values,
the proposed nonadditive approach is found to outper-
form the traditional single-criterion rating approach and
the similarity-based approaches using multicriteria ratings
for V𝐹𝛽, the precision-in-top-3 and the precision-in-top-
5 measures. Moreover, the proposed nonadditive approach
outperforms the additive WAM when using appropriate 𝛽
values for V𝐹𝛽 and different precision-in-top-𝑁 measures.
The experimental results indicate that leveraging the mul-
ticriteria ratings of initiators could be helpful in improving
the prediction performance of the traditional single-criterion
rating approach. In addition, it is found that 𝜆 is less than −0.9
for the best solution. In other words, there exists a substitutive
interaction effect among the attributes. Therefore, it seems
quite reasonable to use the fuzzy integral with a 𝜆-fuzzy
measure as an aggregation function instead of the WAM.
6. Discussion and Conclusions
It is known that the assumption of independence among
criteria in the WAM is not always reasonable. The main
issue that this paper addresses is the additivity of the WAM
for the multicriteria aggregation-function-based approach.
In view of the nonadditivity of the fuzzy integral, this paper
contributes to present a nonadditive aggregation-function-
based approach using multicriteria ratings by combining the
similarity-based approach using single-criterion ratings with
the Choquet fuzzy integral. The former is used to predict mul-
ticriteria ratings and the latter to generate an overall rating for
an item. Because many users of recommendation applications
are typically interested in only the few highest-ranked item
recommendations, a variant of the 𝐹𝛽 measure has been
designed by incorporating the precision-in-top-𝑁 metric
into the 𝐹𝛽 measure to assess prediction performance. Both
the proposed nonadditive approach and the similarity-based
approaches with average/worst-case similarity use the cosine-
based similarity measure to obtain the similarity on each
criterion between two users. Whereas the former (i.e., the
proposed nonadditive approach) derives the rating for each
criterion from individual similarities and then estimates the
overall rating for an item, the latter (i.e., the similarity-based
approaches with average/worst-case similarity) aggregates
the individual similarities to compute the overall similarity
between two users.
The proposed nonadditive approach is applied to initiator
recommendation on a group-buying website in Taiwan in
order to examine its prediction performance. The criterion
weights for the fuzzy integral are determined automatically
by a GA. Compared with the traditional single-criterion
rating approach, several collaborative-filtering approaches
using multicriteria ratings, and the aggregation-function-
based approach using the WAM, it can be seen that the
proposed nonadditive collaborative-filtering approach yields
encouraging V𝐹𝛽, precision-in-top-3, and precision-in-top-5
measures with appropriate 𝛽 values. Therefore, the proposed
approach is able to improve recommendation performance
by leveraging multicriteria information. This indicates that
the proposed nonadditive approach has applicability to other
application domains. Note that the choice of 𝛽 is eventually
dependent on proprietors of websites. Besides, identification
of the best collaborative-filtering approach is not possible
because there is no such thing as the “best” approach [25].
It is notable that, when a traditional single-criterion
rating approach is treated as a baseline collaborative-
filtering approach, the experimental results indicate that
the similarity-based approaches using multicriteria ratings
of initiators perform better than the traditional single-
criterion rating approach. Moreover, the proposed nonad-
ditive approach and the WAM outperform the traditional
single-criterion rating approach with appropriate 𝛽 values.
However, it is not possible to conclude that recommendation
approaches using multicriteria ratings outperform the tradi-
tional single-criterion rating approach in all domains where
multicriteria information exists.
9. Mathematical Problems in Engineering 9
Table 3: Various precisions (%) of WAM and non-additive approach.
Method Precision
𝛽
1 1/2 1/3 1/4 1/5 1/6 1/7 1/8
WAM
Precision-in-top-1 77.01 78.62 79.81 80.72 81.03 81.04 81.66 81.98
Precision-in-top-3 80.09 81.15 81.61 80.96 80.29 81.64 81.37 81.36
Precision-in-top-5 78.37 80.43 81.34 81.25 81.19 82.20 82.46 82.07
Non-additive approach
Precision-in-top-1 76.16 78.84 80.21 83.91 86.16 92.45 90.15 88.44
Precision-in-top-3 76.03 78.19 80.33 82.89 85.32 88.68 88.67 88.58
Precision-in-top-5 74.88 77.68 79.42 83.08 85.50 88.67 88.63 89.14
As mentioned above, the precision-in-top-1 and
precision-in-top-3 measures for the proposed nonadditive
approach are generated by a system that is trained by
incorporating the precision-in-top-5 measure into the fitness
function, whereas the precision-in-top-1 measures obtained
by the proposed nonadditive approach are inferior to those
obtained by approaches using distance-based similarities. It
would be interesting to examine whether the precision-in-
top-1 measure obtained by the proposed approach can be
improved when the system is trained by incorporating the
precision-in-top-1 measure into the fitness function.
Acknowledgments
The author would like to thank the anonymous referees for
their valuable comments. This research is partially supported
by the National Science Council of Taiwan under grant NSC
102-2410-H-033-039-MY2.
References
[1] D. Jannach, M. Zanker, A. Felfernig, and G. Friedrich, Recom-
mender Systems: An Introduction, Cambridge University Press,
New York, NY, USA, 2010.
[2] M. Gao, Z. Wu, and F. Jiang, “Userrank for item-based col-
laborative filtering recommendation,” Information Processing
Letters, vol. 111, no. 9, pp. 440–446, 2011.
[3] S.-L. Huang, “Designing utility-based recommender systems
for e-commerce: evaluation of preference-elicitation methods,”
Electronic Commerce Research and Applications, vol. 10, no. 4,
pp. 398–407, 2011.
[4] S. Opricovic and G.-H. Tzeng, “Compromise solution by
MCDM methods: a comparative analysis of VIKOR and TOP-
SIS,” European Journal of Operational Research, vol. 156, no. 2,
pp. 445–455, 2004.
[5] G. Adomavicius and Y. Kwon, “New recommendation tech-
niques for multicriteria rating systems,” IEEE Intelligent Systems,
vol. 22, no. 3, pp. 48–55, 2007.
[6] G. Adomavicius and A. Tuzhilin, “Toward the next generation
of recommender systems: a survey of the state-of-the-art and
possible extensions,” IEEE Transactions on Knowledge and Data
Engineering, vol. 17, no. 6, pp. 734–749, 2005.
[7] J. B. Schafer, “DynamicLens: a dynamic user-interface for
a meta-recommendation system,” in Proceedings of Beyond
Personalization 2005: A Workshop on the Next Stage of Recom-
mender Systems Research, pp. 72–76.
[8] W.-P. Lee, C.-H. Liu, and C.-C. Lu, “Intelligent agent-based
systems for personalized recommendations in Internet com-
merce,” Expert Systems with Applications, vol. 22, no. 4, pp. 275–
284, 2002.
[9] F. Ricci and H. Werthner, “Case-based querying for travel plan-
ning recommendation,” Information Technology and Tourism,
vol. 4, no. 3-4, pp. 215–226, 2002.
[10] N. Manouselis and C. Costopoulou, “Experimental analysis of
design choices in multi-attribute utility collaborative filtering,”
in Personalization Techniques and Recommender, G. Uchyigit
and M. Y. Ma, Eds., pp. 111–134, World Scientific, River Edge,
NJ, USA, 2008.
[11] T. Onisawa, M. Sugeno, Y. Nishiwaki, H. Kawai, and Y. Harima,
“Fuzzy measure analysis of public attitude towards the use of
nuclear energy,” Fuzzy Sets and Systems, vol. 20, no. 3, pp. 259–
289, 1986.
[12] W. Wang, “Genetic algorithms for determining fuzzy measures
from data,” Journal of Intelligent and Fuzzy Systems, vol. 6, no. 2,
pp. 171–183, 1998.
[13] T. Murofushi and M. Sugeno, “An interpretation of fuzzy
measures and the Choquet integral as an integral with respect
to a fuzzy measure,” Fuzzy Sets and Systems, vol. 29, no. 2, pp.
201–227, 1989.
[14] T. Murofushi and M. Sugeno, “A theory of fuzzy measures:
representations, the Choquet integral, and null sets,” Journal of
Mathematical Analysis and Applications, vol. 159, no. 2, pp. 532–
549, 1991.
[15] T. Murofushi and M. Sugeno, “Some quantities represented by
the Choquet integral,” Fuzzy Sets and Systems, vol. 56, no. 2, pp.
229–235, 1993.
[16] M. Sugeno, Y. Narukawa, and T. Murofushi, “Choquet integral
and fuzzy measures on locally compact space,” Fuzzy Sets and
Systems, vol. 99, no. 2, pp. 205–211, 1998.
[17] Z. Wang, K.-S. Leung, and G. J. Klir, “Applying fuzzy measures
and nonlinear integrals in data mining,” Fuzzy Sets and Systems,
vol. 156, no. 3, pp. 371–380, 2005.
[18] Z. Wang, K.-S. Leung, and J. Wang, “A genetic algorithm for
determining nonadditive set functions in information fusion,”
Fuzzy Sets and Systems, vol. 102, no. 3, pp. 463–469, 1999.
[19] C. Desrosiers and G. Karypis, “A comprehensive survey of
neighborhood-based recommendation methods,” in Recom-
mender Systems Handbook, F. Ricci, L. Rokach, B. Shapira, and
P. B. Kantor, Eds., pp. 107–144, Springer, New York, NY, USA,
2011.
[20] J. A. Konstan, B. N. Miller, D. Maltz, J. L. Herlocker, L. R.
Gordon, and J. Riedl, “Applying collaborative filtering to usenet
news,” Communications of the ACM, vol. 40, no. 3, pp. 77–87,
1997.
10. 10 Mathematical Problems in Engineering
[21] J. Herlocker, J. Konstan, A. Borchers, and J. Riedl, “An algo-
rithmic framework for performing collaborative filtering,” in
Proceedings of the 22nd Annual International ACM SIGIR Con-
ference on Research and Development in Information Retrieval,
pp. 230–237, 1999.
[22] M. Sugeno, Theory of fuzzy integrals and its applications [Ph.D.
thesis], Tokyo Institute of Technology, Tokyo, Japan, 1974.
[23] M. Sugeno, “Fuzzy measures and fuzzy integrals—a survey,”
in Fuzzy Automata and Decision Processes, pp. 89–102, North-
Holland, New York, NY, USA, 1977.
[24] Z. Y. Wang and G. J. Klir, Fuzzy Measure Theory, Plenum Press,
New York, NY, USA, 1992.
[25] L. I. Kuncheva, Fuzzy Classifier Design, Physica, Heidelberg,
Germany, 2000.
[26] C. J. van Rijsbergen, Information Retrieval, Butterworth, Lon-
don, UK, 1979.
[27] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and
Machine Learning, Addison-Wesley, Reading, Mass, USA, 1989.
[28] K. F. Man, K. S. Tang, and S. Kwong, Genetic Algorithms:
Concepts and Designs, Springer, London, UK, 1999.
[29] B. I. A. Kelsey, 2011, http://www.biakelsey.com.
[30] “Foreseeing Innovative New Digiservices in Institute for
Information Industry,” 2011, http://www.find.org.tw/find/home
.aspx?page=many&id=290.
[31] J. Singh and D. Sirdeshmukh, “Agency and trust mechanisms
in consumer satisfaction and loyalty judgments,” Journal of the
Academy of Marketing Science, vol. 28, no. 1, pp. 150–167, 2000.
[32] S. Ganesan, “Determinants of long-term orientation in buyer-
seller relationships,” Journal of Marketing, vol. 58, pp. 1–19, 1994.
[33] C. M. Ridings, D. Gefen, and B. Arinze, “Some antecedents
and effects of trust in virtual communities,” Journal of Strategic
Information Systems, vol. 11, no. 3-4, pp. 271–295, 2002.
[34] D. M. Rousseau, S. Sitkin, R. S. Burt, and C. Camerer, “Not so
different after all: a cross-discipline view of trust,” Academy of
Management Review, vol. 23, pp. 393–404, 1998.
[35] P. M. Doney and J. P. Cannon, “An examination of the nature of
trust in buyer-seller relationships,” Journal of Marketing, vol. 61,
no. 2, pp. 35–51, 1997.
[36] A. Osyczka, Evolutionary Algorithms for Single and Multicriteria
Design Optimization, Physica, New York, NY, USA, 2002.
[37] H. Ishibuchi, T. Nakashima, and M. Nii, Classification and
Modeling with Linguistic Information Granules: Advanced
Approaches to Linguistic Data Mining, Springer, 2004.
11. Submit your manuscripts at
http://www.hindawi.com
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Mathematics
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Mathematical Problems
in Engineering
Hindawi Publishing Corporation
http://www.hindawi.com
Differential Equations
International Journal of
Volume 2014
Applied Mathematics
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Probability and Statistics
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Mathematical Physics
Advances in
Complex Analysis
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Optimization
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Combinatorics
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
International Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Operations Research
Advances in
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Function Spaces
Abstract and
Applied Analysis
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
International
Journal of
Mathematics and
Mathematical
Sciences
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
The Scientific
World Journal
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Algebra
Discrete Dynamics in
Nature and Society
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Decision Sciences
Advances in
DiscreteMathematics
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014 Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Stochastic Analysis
International Journal of