Failure mode and effects analysis (FMEA) is awidely used engineering technique for designing, identifying
and eliminating theknown and/or potential failures, problems, and errors and so on from system to other
parts. The evaluating of FMEA parameters is challenging point because it’s importantfor managers to
know the real risk in their systems. In this study,we used fuzzy TODIM for evaluating the potential failure
modes in our system respect to factors of FMEA,which is known as; Severity(S); Occurrence (O); and
detect ability (D).The final result was combined with fuzzy time function which helps to predict systems in
future and solving problems in our system and it could help to avoid potential future failure modes in our
systems.
Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) have shown popularity, superiority, and more accuracy in performance in a number of applications in the last decade. This is due to its ability to cope with uncertainty and precisions adequately when compared with its type-1 counterpart. In this paper, an Interval Type-2 Fuzzy Logic System (IT2FLS) is employed for remote vital signs monitoring and predicting of shock level in cardiac patients. Also, the conventional, Type-1 Fuzzy Logic System (T1FLS) is applied to the prediction problems for comparison purpose. The cardiac patients’ health datasets were used to perform empirical comparison on the developed system. The result of study indicated that IT2FLS could coped with more information and handled more uncertainties in health data than T1FLS. The statistical evaluation using performance metrices indicated a minimal error with IT2FLS compared to its counterpart, T1FLS. It was generally observed that the shock level prediction experiment for cardiac patients showed the superiority of IT2FLS paradigm over T1FLS.
Collocation Extraction Performance Ratings Using Fuzzy logicWaqas Tariq
The performance of Collocation extraction cannot quantified or properly express by a single dimension. It is very imprecise to interpret collocation extraction metrics without knowing what application (users) are involved. Most of the existing collocation extraction techniques are of Berry-Roughe, Church and Hanks, Kita, Shimohata, Blaheta and Johnson, and Pearce. The extraction techniques need to be frequently updated based on feedbacks from implementation of previous policies. These feedbacks are always stated in the form of ordinal ratings, e.g. “high speed”, “average performance”, “good condition”. Different people can describe different values to these ordinal ratings without a clear-cut reason or scientific basis. There is need for a way or means to transform vague ordinal ratings to more appreciable and precise numerical estimates. The paper transforms the ordinal performance ratings of some Collocation performance techniques to numerical ratings using Fuzzy logic. Keywords: Fuzzy Set Theory, collocation extraction, Transformation, performance Techniques, Criteria.
Decision trees have been widely used in machine learning. However, due to some reasons, data collecting
in real world contains a fuzzy and uncertain form. The decision tree should be able to handle such fuzzy
data. This paper presents a method to construct fuzzy decision tree. It proposes a fuzzy decision tree
induction method in iris flower data set, obtaining the entropy from the distance between an average value
and a particular value. It also presents an experiment result that shows the accuracy compared to former
ID3.
Integrating Fuzzy Dematel and SMAA-2 for Maintenance Expensesinventionjournals
The majority of the allowances being transferred to public institutions are mostly spent for buying new equipment, materials, facilities and their maintenance and repair. Some of the public sectors establish their own plants in order to reduce the maintenance and repair costs and gain ability to perform these activities. However, developing technology and variety of materials make their repair and maintenance activities more expensive for them. In this study, vital criteria for a public institution are determined. By using Fuzzy DEMATEL (Decision Making Trial And Evaluation Laboratory) method the degree of importance is identified by two defuzzification methods and the alternatives are ranked by using SMAA-2 (Stochastic Multi Criteria Acceptability Analysis) in three scenarios. The results show that different defuzzification methods change the order of preferences.
INTERVAL TYPE-2 INTUITIONISTIC FUZZY LOGIC SYSTEM FOR TIME SERIES AND IDENTIF...ijfls
This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.
Human Resource Recruitment using Fuzzy Decision Making MethodIJSRD
Traditional way of recruiting personnel was through a group decision making problem under multiple criteria containing subjectivity, imprecision and vagueness. In order to keep up with increasing competition of globalization and fast technological improvements and changes, Human resource field needs the best fit employee for a job vacancy. This paper proposes a Fuzzy Decision Making (FDM) method for recruitment process of Human Resource management, which is based on the Fuzzy set theory. Different criteria of human resource recruitment process will be given fuzzy linguistic terms such as absolutely low, extremely low, very low, low, medium, high, very high, extremely high, absolutely high depends upon the importance given by the Human Resource manager. Fuzzy Scaled Weight (FSW) will be calculated for all the criteria. Cumulative Fuzzy Value (CFV) is calculated for all the applicants from Fuzzy Scaled Weight values. Interview Fuzzy Value (IFV) is given by the human resource manager for all the applicants attending interviews. Final Fuzzy Value (FFV) will be calculated aggregating both Cumulative Fuzzy Value and Interview Fuzzy Value. Finally, all the applicant records are arranged in the order of FFV values. Then, Human resource manager can select the applicants easily from the arranged list. Fuzzy Decision Making method system is developed to illustrate the above FDM method for the Human Resource recruitment process.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
In the present paper a numerical attempt is made to study the combined effects of heat source and sink on unsteady laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid along a semiinfinite vertical plate. A magnetic field of uniform strength is applied normal to the flow. The governing boundary layer equations are solved numerically, using Crank-Nicolson method. Graphical results of velocity and temperature fields, tabular values of Skin-friction and Nusselt are presented and discussed at various parametric conditions. From this study, it is found that the velocity and temperature of the fluid increase in the presence of heat source but they decrease in the presence of heat absorption parameter.
Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) have shown popularity, superiority, and more accuracy in performance in a number of applications in the last decade. This is due to its ability to cope with uncertainty and precisions adequately when compared with its type-1 counterpart. In this paper, an Interval Type-2 Fuzzy Logic System (IT2FLS) is employed for remote vital signs monitoring and predicting of shock level in cardiac patients. Also, the conventional, Type-1 Fuzzy Logic System (T1FLS) is applied to the prediction problems for comparison purpose. The cardiac patients’ health datasets were used to perform empirical comparison on the developed system. The result of study indicated that IT2FLS could coped with more information and handled more uncertainties in health data than T1FLS. The statistical evaluation using performance metrices indicated a minimal error with IT2FLS compared to its counterpart, T1FLS. It was generally observed that the shock level prediction experiment for cardiac patients showed the superiority of IT2FLS paradigm over T1FLS.
Collocation Extraction Performance Ratings Using Fuzzy logicWaqas Tariq
The performance of Collocation extraction cannot quantified or properly express by a single dimension. It is very imprecise to interpret collocation extraction metrics without knowing what application (users) are involved. Most of the existing collocation extraction techniques are of Berry-Roughe, Church and Hanks, Kita, Shimohata, Blaheta and Johnson, and Pearce. The extraction techniques need to be frequently updated based on feedbacks from implementation of previous policies. These feedbacks are always stated in the form of ordinal ratings, e.g. “high speed”, “average performance”, “good condition”. Different people can describe different values to these ordinal ratings without a clear-cut reason or scientific basis. There is need for a way or means to transform vague ordinal ratings to more appreciable and precise numerical estimates. The paper transforms the ordinal performance ratings of some Collocation performance techniques to numerical ratings using Fuzzy logic. Keywords: Fuzzy Set Theory, collocation extraction, Transformation, performance Techniques, Criteria.
Decision trees have been widely used in machine learning. However, due to some reasons, data collecting
in real world contains a fuzzy and uncertain form. The decision tree should be able to handle such fuzzy
data. This paper presents a method to construct fuzzy decision tree. It proposes a fuzzy decision tree
induction method in iris flower data set, obtaining the entropy from the distance between an average value
and a particular value. It also presents an experiment result that shows the accuracy compared to former
ID3.
Integrating Fuzzy Dematel and SMAA-2 for Maintenance Expensesinventionjournals
The majority of the allowances being transferred to public institutions are mostly spent for buying new equipment, materials, facilities and their maintenance and repair. Some of the public sectors establish their own plants in order to reduce the maintenance and repair costs and gain ability to perform these activities. However, developing technology and variety of materials make their repair and maintenance activities more expensive for them. In this study, vital criteria for a public institution are determined. By using Fuzzy DEMATEL (Decision Making Trial And Evaluation Laboratory) method the degree of importance is identified by two defuzzification methods and the alternatives are ranked by using SMAA-2 (Stochastic Multi Criteria Acceptability Analysis) in three scenarios. The results show that different defuzzification methods change the order of preferences.
INTERVAL TYPE-2 INTUITIONISTIC FUZZY LOGIC SYSTEM FOR TIME SERIES AND IDENTIF...ijfls
This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.
Human Resource Recruitment using Fuzzy Decision Making MethodIJSRD
Traditional way of recruiting personnel was through a group decision making problem under multiple criteria containing subjectivity, imprecision and vagueness. In order to keep up with increasing competition of globalization and fast technological improvements and changes, Human resource field needs the best fit employee for a job vacancy. This paper proposes a Fuzzy Decision Making (FDM) method for recruitment process of Human Resource management, which is based on the Fuzzy set theory. Different criteria of human resource recruitment process will be given fuzzy linguistic terms such as absolutely low, extremely low, very low, low, medium, high, very high, extremely high, absolutely high depends upon the importance given by the Human Resource manager. Fuzzy Scaled Weight (FSW) will be calculated for all the criteria. Cumulative Fuzzy Value (CFV) is calculated for all the applicants from Fuzzy Scaled Weight values. Interview Fuzzy Value (IFV) is given by the human resource manager for all the applicants attending interviews. Final Fuzzy Value (FFV) will be calculated aggregating both Cumulative Fuzzy Value and Interview Fuzzy Value. Finally, all the applicant records are arranged in the order of FFV values. Then, Human resource manager can select the applicants easily from the arranged list. Fuzzy Decision Making method system is developed to illustrate the above FDM method for the Human Resource recruitment process.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
In the present paper a numerical attempt is made to study the combined effects of heat source and sink on unsteady laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid along a semiinfinite vertical plate. A magnetic field of uniform strength is applied normal to the flow. The governing boundary layer equations are solved numerically, using Crank-Nicolson method. Graphical results of velocity and temperature fields, tabular values of Skin-friction and Nusselt are presented and discussed at various parametric conditions. From this study, it is found that the velocity and temperature of the fluid increase in the presence of heat source but they decrease in the presence of heat absorption parameter.
ANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRET...ijsc
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers
are commonly performed. Aggregation and defuzzification operations are some of these often used
operations. Many aggregation and defuzzification operators produce results independent to the decisionmaker’s
strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take
into account the level weights and the decision maker's "optimism" strategy. This gives flexibility to the
WABL operator and, through machine learning, can be trained in the direction of the decision maker's
strategy, producing more satisfactory results for the decision maker. However, in order to determine the
WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete
trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the
calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy
numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers
have been studied. Computational examples explaining the theoretical results have been performed.
I Planned to give a specific training on Fuzzy Logic Controller using MATLAB simulation. This type of intelligent controller is very useful for the research work in all discipline.
At the end of learning at an educational level, leaders often perceive difficulties in
determining the best students at a certain level of education. Cumulative Achievement Index may
not be used for decision makers in determining the best students. There are criteria other criteria that
influence them are actively organize, have never done a repair value, never follow short semester,
never leave. Using these criteria and using Multi-Criteria Decision Making (MCDM) based methods
applied to decision support systems can deliver the expected outcomes of higher education leaders.
Many methods can be used on decision support systems such as Promethee, Promethee II, Electre,
AHP, SAW, or TOPSIS. In this discussion, the author uses Extended Promethee II method in
determining the best student at a college.
Face Recognition System Using Local Ternary Pattern and Signed Number Multipl...inventionjournals
This paper presents a novel approach to face recognition. The task of face recognition is to verify a claimed identity by comparing a claimed image of the individual with other images belonging to the same individual/other individual in a database. The proposed method utilizes Local Ternary Pattern and signed bit multiplication to extract local features of a face. The image is divided into small non-overlapping windows. Processing is carried out on these windows to extract features. Test image’s features are compared with all the training images using Euclidean's distance. The image with lowest Euclidean distance is recognized as the true face image. If the distance between test and all training images is more than threshold then test image is considered as unrecognised image or match not found .The face recognition rate of proposed system is calculated by varying the number of images per person in training database
This presentation talks about some of the outstanding methods for Interpreting the complex machine learning black box models. One of the ideas is to use interpretable simple models to explain predictions using sophisticated black box machine learning models.
Model Agnostic methods are proven to have some specific advantages over the Model Specific Methods of Interpretability. This work demonstrates some of such results.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
Toward a Natural Genetic / Evolutionary Algorithm for Multiobjective Optimiza...Startup
New Genetic or Evolutionary Algorithm for multiobjective optimization, that attempts to find tradeoff solutions and scales easily with increase in parameter space as well as objective space. Does not use complex niche calculation that is used in existing multiobjective genetic algorithms.
In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian’s (2014) method is reviewed. Finally, the comparative study, results and discussion are given.
An Interval Type-2 Fuzzy Approach for Process Plan Selectioninventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The Fuzzy set Theory has been applied in many fields such as Management, Engineering etc. In this paper a new operation on Hexagonal Fuzzy number is defined where the methods of addition, subtraction, and multiplication has been modified with some conditions. The main aim of this paper is to introduce a new operation for addition, subtraction and multiplication of Hexagonal Fuzzy number on the basis of alpha cut sets of fuzzy numbers
Importance of the neutral category in fuzzy clustering of sentimentsijfls
Social media is said to have an impact on the public discourse and communication in the society. It is increasingly
being used in the political context. Social networks sites such as Facebook, Twitter and other
microblogging services provide an opportunity for public to give opinions about some issues of interest.
Twitter is an ideal platform for users to spread not only information in general but also political opinions,
whereas Facebook provides the capability for direct dialogs. A lot of studies have shown that a need exists
for stakeholders to collect, monitor, analyze, summarize and visualize these social media views. Some authors
have tended to categorize these comments as either positive or negative ignoring the neutral category.
In this paper, we demonstrate the importance of the neutral category in the clustering of sentiments
from the social media. We then demonstrate the use of fuzzy clustering for this kind of task.
APPLICATION OF FUZZY LOGIC TO VISUAL EXAMINATION IN THE ASSESSMENT OF SULPHAT...ijfls
Sulphate attack on cement based materials has been widely taken up in research studies focusing on
aggressive environmental conditions. Visual observations are considered as an important first step to
assess the performance of the materials under the severity of the involved conditions. Correlations of visual
observations (supported by other tests, during controlled laboratory experiments) and conditions in the
field are essential to assess the performance of materials in the field. Due to uncertainties in the
determination of various performance related parameters in the field, a rigid reliance on the results of
visual examination conducted in the laboratory is not possible. This paper considers some aspects related
to visual observations concerning the performance assessment of cement based materials under sulphate
attack conditions in the field. Through a theoretical study it explores the use of fuzzy logic in analysing how
much reasonable confidence should be placed on visual observations as well as in determining relative
importance of various parameters
This paper investigates fuzzy triangle and similarity of fuzzy triangles. Five rules to determine similarity of
fuzzy triangles are studied. Extension principle and concept of same and inverse points in fuzzy geometry
are used to analyze the proposed concepts.
Doubt intuitionistic fuzzy deals in bckbci algebrasijfls
In this paper, we introduce the concept of doubt intuitionistic fuzzy subalgebras and doubt intuitionistic fuzzy ideals in BCK/BCI-algebras. We show that an intuitionistic fuzzy subset of BCK/BCI-algebras is an
intuitionistic fuzzy subalgebra and an intuitionistic fuzzy ideal if and only if the complement of this intuitionistic fuzzy subset is a doubt intuitionistic fuzzy subalgebra and a doubt intuitionistic fuzzy ideal. And at the same time we have established some common properties related to them.
This paper suggests an effective method for facial recognition using fuzzy theory and Shannon entropy.
Combination of fuzzy theory and Shannon entropy eliminates the complication of other methods. Shannon
entropy calculates the ratio of an element between faces, and fuzzy theory calculates the membership of the
entropy with 1. More details will be mentioned in Section 3. The learning performance is better than others
as it is very simple, and only need two data per learning. By using factors that don’t usually change during
the life, the method will have a high accuracy.
ANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRET...ijsc
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers
are commonly performed. Aggregation and defuzzification operations are some of these often used
operations. Many aggregation and defuzzification operators produce results independent to the decisionmaker’s
strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take
into account the level weights and the decision maker's "optimism" strategy. This gives flexibility to the
WABL operator and, through machine learning, can be trained in the direction of the decision maker's
strategy, producing more satisfactory results for the decision maker. However, in order to determine the
WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete
trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the
calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy
numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers
have been studied. Computational examples explaining the theoretical results have been performed.
I Planned to give a specific training on Fuzzy Logic Controller using MATLAB simulation. This type of intelligent controller is very useful for the research work in all discipline.
At the end of learning at an educational level, leaders often perceive difficulties in
determining the best students at a certain level of education. Cumulative Achievement Index may
not be used for decision makers in determining the best students. There are criteria other criteria that
influence them are actively organize, have never done a repair value, never follow short semester,
never leave. Using these criteria and using Multi-Criteria Decision Making (MCDM) based methods
applied to decision support systems can deliver the expected outcomes of higher education leaders.
Many methods can be used on decision support systems such as Promethee, Promethee II, Electre,
AHP, SAW, or TOPSIS. In this discussion, the author uses Extended Promethee II method in
determining the best student at a college.
Face Recognition System Using Local Ternary Pattern and Signed Number Multipl...inventionjournals
This paper presents a novel approach to face recognition. The task of face recognition is to verify a claimed identity by comparing a claimed image of the individual with other images belonging to the same individual/other individual in a database. The proposed method utilizes Local Ternary Pattern and signed bit multiplication to extract local features of a face. The image is divided into small non-overlapping windows. Processing is carried out on these windows to extract features. Test image’s features are compared with all the training images using Euclidean's distance. The image with lowest Euclidean distance is recognized as the true face image. If the distance between test and all training images is more than threshold then test image is considered as unrecognised image or match not found .The face recognition rate of proposed system is calculated by varying the number of images per person in training database
This presentation talks about some of the outstanding methods for Interpreting the complex machine learning black box models. One of the ideas is to use interpretable simple models to explain predictions using sophisticated black box machine learning models.
Model Agnostic methods are proven to have some specific advantages over the Model Specific Methods of Interpretability. This work demonstrates some of such results.
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
Toward a Natural Genetic / Evolutionary Algorithm for Multiobjective Optimiza...Startup
New Genetic or Evolutionary Algorithm for multiobjective optimization, that attempts to find tradeoff solutions and scales easily with increase in parameter space as well as objective space. Does not use complex niche calculation that is used in existing multiobjective genetic algorithms.
In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian’s (2014) method is reviewed. Finally, the comparative study, results and discussion are given.
An Interval Type-2 Fuzzy Approach for Process Plan Selectioninventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The Fuzzy set Theory has been applied in many fields such as Management, Engineering etc. In this paper a new operation on Hexagonal Fuzzy number is defined where the methods of addition, subtraction, and multiplication has been modified with some conditions. The main aim of this paper is to introduce a new operation for addition, subtraction and multiplication of Hexagonal Fuzzy number on the basis of alpha cut sets of fuzzy numbers
Importance of the neutral category in fuzzy clustering of sentimentsijfls
Social media is said to have an impact on the public discourse and communication in the society. It is increasingly
being used in the political context. Social networks sites such as Facebook, Twitter and other
microblogging services provide an opportunity for public to give opinions about some issues of interest.
Twitter is an ideal platform for users to spread not only information in general but also political opinions,
whereas Facebook provides the capability for direct dialogs. A lot of studies have shown that a need exists
for stakeholders to collect, monitor, analyze, summarize and visualize these social media views. Some authors
have tended to categorize these comments as either positive or negative ignoring the neutral category.
In this paper, we demonstrate the importance of the neutral category in the clustering of sentiments
from the social media. We then demonstrate the use of fuzzy clustering for this kind of task.
APPLICATION OF FUZZY LOGIC TO VISUAL EXAMINATION IN THE ASSESSMENT OF SULPHAT...ijfls
Sulphate attack on cement based materials has been widely taken up in research studies focusing on
aggressive environmental conditions. Visual observations are considered as an important first step to
assess the performance of the materials under the severity of the involved conditions. Correlations of visual
observations (supported by other tests, during controlled laboratory experiments) and conditions in the
field are essential to assess the performance of materials in the field. Due to uncertainties in the
determination of various performance related parameters in the field, a rigid reliance on the results of
visual examination conducted in the laboratory is not possible. This paper considers some aspects related
to visual observations concerning the performance assessment of cement based materials under sulphate
attack conditions in the field. Through a theoretical study it explores the use of fuzzy logic in analysing how
much reasonable confidence should be placed on visual observations as well as in determining relative
importance of various parameters
This paper investigates fuzzy triangle and similarity of fuzzy triangles. Five rules to determine similarity of
fuzzy triangles are studied. Extension principle and concept of same and inverse points in fuzzy geometry
are used to analyze the proposed concepts.
Doubt intuitionistic fuzzy deals in bckbci algebrasijfls
In this paper, we introduce the concept of doubt intuitionistic fuzzy subalgebras and doubt intuitionistic fuzzy ideals in BCK/BCI-algebras. We show that an intuitionistic fuzzy subset of BCK/BCI-algebras is an
intuitionistic fuzzy subalgebra and an intuitionistic fuzzy ideal if and only if the complement of this intuitionistic fuzzy subset is a doubt intuitionistic fuzzy subalgebra and a doubt intuitionistic fuzzy ideal. And at the same time we have established some common properties related to them.
This paper suggests an effective method for facial recognition using fuzzy theory and Shannon entropy.
Combination of fuzzy theory and Shannon entropy eliminates the complication of other methods. Shannon
entropy calculates the ratio of an element between faces, and fuzzy theory calculates the membership of the
entropy with 1. More details will be mentioned in Section 3. The learning performance is better than others
as it is very simple, and only need two data per learning. By using factors that don’t usually change during
the life, the method will have a high accuracy.
A Counterexample to the Forward Recursion in Fuzzy Critical Path Analysis Und...ijfls
Fuzzy logic is an alternate approach for quantifying uncertainty relating to activity duration. The fuzzy
version of the backward recursion has been shown to produce results that incorrectly amplify the level of
uncertainty. However, the fuzzy version of the forward recursion has been widely proposed as an
approach for determining the fuzzy set of critical path lengths. In this paper, the direct application of the
extension principle leads to a proposition that must be satisfied in fuzzy critical path analysis. Using a
counterexample it is demonstrated that the fuzzy forward recursion when discrete fuzzy sets are used to
represent activity durations produces results that are not consistent with the theory presented. The
problem is shown to be the application of the fuzzy maximum. Several methods presented in the literature
are described and shown to provide results that are consistent with the extension principle.
Parameters Optimization for Improving ASR Performance in Adverse Real World N...Waqas Tariq
From the existing research it has been observed that many techniques and methodologies are available for performing every step of Automatic Speech Recognition (ASR) system, but the performance (Minimization of Word Error Recognition-WER and Maximization of Word Accuracy Rate- WAR) of the methodology is not dependent on the only technique applied in that method. The research work indicates that, performance mainly depends on the category of the noise, the level of the noise and the variable size of the window, frame, frame overlap etc is considered in the existing methods. The main aim of the work presented in this paper is to use variable size of parameters like window size, frame size and frame overlap percentage to observe the performance of algorithms for various categories of noise with different levels and also train the system for all size of parameters and category of real world noisy environment to improve the performance of the speech recognition system. This paper presents the results of Signal-to-Noise Ratio (SNR) and Accuracy test by applying variable size of parameters. It is observed that, it is really very hard to evaluate test results and decide parameter size for ASR performance improvement for its resultant optimization. Hence, this study further suggests the feasible and optimum parameter size using Fuzzy Inference System (FIS) for enhancing resultant accuracy in adverse real world noisy environmental conditions. This work will be helpful to give discriminative training of ubiquitous ASR system for better Human Computer Interaction (HCI). Keywords: ASR Performance, ASR Parameters Optimization, Multi-Environmental Training, Fuzzy Inference System for ASR, ubiquitous ASR system, Human Computer Interaction (HCI)
GROUP FUZZY TOPSIS METHODOLOGY IN COMPUTER SECURITY SOFTWARE SELECTIONijfls
In today's interconnected world, the risk of malwares is a major concern for users. Antivirus software is a
device to prevent, discover, and eliminatemalwares such as, computer worm, trojan horses,computer
viruses,spyware and adware. In the competitive IT environment, due to availability of many antivirus
software and their diverse features evaluating them is an arguable and complicated issue for users which
has a significant impact on the efficiency of computers defense systems. The anti-virus selection problem
can be formulated as a multiple criteria decision making problem. This paper proposes an antivirus
evaluation model for computer users based on group fuzzy TOPSIS. We study a real world case of antivirus
software and define criteria for antivirus selection problem. Seven alternatives were selected from among
the most popular antiviruses in the market and seven criteria were determined by the experts. The study is
followed by the sensitivity analyses of the results which also gives valuable insights into the needs and
solutions for different users in different conditions.
SPECIFICATION OF THE STATE’S LIFETIME IN THE DEVS FORMALISM BY FUZZY CONTROLLERijait
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specify a fuzzy model which computes this duration, this latter is fed into the simulator to specify the new
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condition, and various variables involved. A global specification of the fuzzy controller and the forest fire
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of signal to be decomposed, and construct the parameter equation with the amplitude and initial phase of signal
as unknowns. Second, employing particle swarm optimization (PSO) to estimate the unknown parameters, and
extending the inspected signal according to the obtained parameters. Thirdly, using EMD to decompose the
extended signal into a series of intrinsic mode functions (IMFs) and a residual. The IMFs of original signal are
extracted from these obtained IMFs. The correlation coefficients between the IMFs and the signal are calculated
to judge the pseudo-IMFs. The simulation result shows that the presented method is effective and extends the
application of EMD.
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group decision making (MAGDM) technique for helping the health-care department to choose a suitable
diagnostic laboratory among several alternatives. In the process of decision making, experts provide
linguistic terms to evaluate each of the alternatives, which are parameterized by generalized triangular
fuzzy numbers (GTFNs). Subsequently fuzzy MAGDM method is applied to determine the overall
performance value for each alternative (laboratory) to make a final decision. Finally, the diagnostic
laboratory evaluation problem is presented involving seven evaluation attributes, five laboratories and five
experts.
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NEURAL NETWORK BASED SUPERVISED SELF ORGANIZING MAPS FOR FACE RECOGNITIONijsc
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and verify the identity of an individual. Face is one of the human biometrics for passive identification with
uniqueness and stability. In this manuscript we present a new face based biometric system based on neural
networks supervised self organizing maps (SOM). We name our method named SOM-F. We show that the
proposed SOM-F method improves the performance and robustness of recognition. We apply the proposed
method to a variety of datasets and show the results.
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4. Demo
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UiPath Test Automation using UiPath Test Suite series, part 4
A new analysis of failure modes and effects by fuzzy todim with using fuzzy time function
1. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
DOI : 10.5121/ijfls.2014.4202 7
A NEW ANALYSIS OF FAILURE MODES AND
EFFECTS BY FUZZY TODIM WITH USING
FUZZY TIME FUNCTION
M.Mahmoodi & A. Mirzazadeh
Aboulfazl.Mirzazadeh, PHD, Department of Industrial engineering, Kharazmi
University, Tehran, Iran
Mahdi.Mahmoodi, Ms.Student, Department of Industrial engineering, Kharazmi
University, Tehran, Iran
ABSTRACT
Failure mode and effects analysis (FMEA) is awidely used engineering technique for designing, identifying
and eliminating theknown and/or potential failures, problems, and errors and so on from system to other
parts. The evaluating of FMEA parameters is challenging point because it’s importantfor managers to
know the real risk in their systems. In this study,we used fuzzy TODIM for evaluating the potential failure
modes in our system respect to factors of FMEA,which is known as; Severity(S); Occurrence (O); and
detect ability (D).The final result was combined with fuzzy time function which helps to predict systems in
future and solving problems in our system and it could help to avoid potential future failure modes in our
systems.
KEYWORDS
Fuzzy FMEA, Fuzzy set theory, Fuzzy TODIM, Fuzzy time function.
1. INTRODUCTION
Failure mode and effects is one of the subjects in organization and factories which can help
decreasing the cost and improving effectiveness in system. FMEA, provides a framework or
cause and effect analysis of potential product failures. Chin, Chan& Yang,2008 [1] has a purpose
of prioritizing the risk priority number (RPN) of the product design or planning process to assign
the limited resources to the most serious risk item. FMEA, designed to provide information for
risk management formal design methodology by NASA in 1963 for their obvious reliability
requirements and then, it was adopted and promoted by Ford Motor in 1977 (Chin et al,2008)[1].
Since then, it has become a powerful tool extensively used for safety and reliability analysis of
products and process in a wide range of industries especially aerospace, nuclear and automotive
industries (Gilchrist, 1993 [2]; Sharma, Kumar 2005 [3]) and these kinds of research shows the
impotency of FMEA in industrials.
2. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
8
Ben-Daya & Raouf,(1996)[4],Each failure mode can be evaluated by three factors as severity,
likelihood of occurrence, and the difficulty of detection of the failure mode .In a typical FMEA
evaluation , a number between 1 and 10 (with 1 being the best and 10 being the worst case) is
given for each of the three factors. By multiplying the values for severity (S), occurrence (O), and
detect ability (D), a risk priority number (RPN) is obtained, which is RPN=S×O×D (Chin et
al,2008).Then the RPN value for each failure mode is ranked to find out the failures with higher
risks.
The base values of RPNs have been considerably criticized for many reasons, most of them are
stated below:
• The relative importance among the three risk factors occurrence, severity, and detection
is not considered as they are accepted equally important.
• Different combination of O, S and D may produce exactly the same value of RPN,
although their hidden risk implications may be totally different. For instance, two
different failures with the O, S and D values of 4, 3, 3 and 9, 1, 3, respectively, have the
same RPN value of 36.
• The use of multiplication method in the calculation of RPN is questionable and strongly
sensitive to variations in criticality factor evaluations.
When the traditional FMEA and the fuzzy approach are compared, the fuzzy approach has an
advantage of allowing the conduction of risk evaluation and prioritization based on the
knowledge of the experts (Tay & Lim 2006) [5].
Xu, Tang, Xie, Ho, and Zhu (2002) [6], state the reasons for considering the fuzzy logic approach
as following:
• All FMEA-related information is taken in natural language which is easy and plausible
for fuzzy logic to deal with as it is based on human language and can be built on top of
the experience of experts.
• Fuzzy logic allows imprecise data usage so it enables the treatment of many states.
In this study we collect data from experts with fuzzy linguistic numbers, this data shows
each potential failure modes in our systems respect to the three risk factors of FMEA, and
then we used fuzzy TODIM for ranking this alternatives and factors of FMEA. In final
steps we used fuzzy time function for considering time in our decisions making for
future, and with combination of fuzzy time function and Todim, the final results shown in
our study.
2. METHODOLOGY
2.1. Fuzzy FMEA
Significant efforts have been made in FMEA literature to overcome the shortcomings of the
traditional RPN ,Wang et al, 2009[7].The studies about FMEA considering fuzzy approach use
the experts who describe the risk factors O, S, and D by using the fuzzy linguistic terms. The
linguistic variables were used for evaluating the risk factors against the alternative. This helps to
reduce calculations and do the same way Fuzzy AHP and TOPSIS Fuzzy do with this benefit to
3. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
9
determine in one step. The linguistic variables as an interpretation of traditional FMEA are in 10
point scale. (1-10)
Criteria
Severity S
occurrence O
Detect ability D
Table 1. Criteria
2.2. Fuzzy Logic
A fuzzy set is a class of objects with grades of membership. A membership function is between
zero and one, Zadeh, 1965, [8].Fuzzy logic is derived from fuzzy set theory to deal with
reasoning that is approximate rather than precise. It allows the model to easily incorporate various
subject experts’ advice in developing critical parameter estimates, Zimmermann, 2001[9].In other
words; fuzzy logic enables us to handle uncertainty.
There are some kinds of fuzzy numbers. Among the various shapes of fuzzy number, triangular
fuzzy number (TFN) is the most popular one. It is represented with three points asbellow: a= (a1,
a2, a3). The membership function is illustrated in Eq. (1).
Let A and B are defined as a= (a1, a2,a3), b= (b1,b2,b3). Then c= (a1+b1,a2+b2,a3+b3) is the
addition of these two numbers. Besides, d= (a1-b3,a2-b2,a3-b1) is the subtraction of them.
Moreover, d= (a1.b1 ,a2.b2,a3.b3) is the multiplication of them (Klir& Yean, 1995[10]; Lai &
Hwang; 1995[11]; Zimmermann, 2001[9]).
Ahmet et al.2012[12], used triangular fuzzy number to collect data ,and then used fuzzy Topsis to
evaluate data which we used here interval valued fuzzy number and TODIM ,and we get better
results.
This study use interval-valued triangular fuzzy for collecting expert’s opinion (Table .2)
Linguistic
preferences
Interval-valued TFNS
Very poor [(0,0),0,(1,1.5)]
Poor [(0,0.5),1,(2.5,3.5)]
Medium poor [(0,1.5),3,(4.5,5.5)]
Fair [(2.5,3.5),5,(6.5,7.5)]
Medium good [(4.5,5.5),7,(8,9.5)]
Good [(5.5,7.5),9,(9.5,10)]
Very good [(8.5,9.5),10,(10,10)]
Table 2.corresponding TFNS to linguistic preferences.
Definition 1. A TFN a is defined by a triangular with membership function:
4. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
10
Definition 2. The distance between a and b is:
2 2 2
1 1 2 2 3 3
1
( ) [( ) ( ) ( ) ] (2)
3
a b a b a b a bδ + = − + − + −
The TFN is based on a three-value judgment: the minimum possible vale a1 , the mean value a2
and the maximum possible value a3. The criteria values depend on linguistic preferences.
The weight vector w= (w1,w2,w3) of the three factors of FMEA is unknown but satisfies wj≥0 ,
j=1,2, 3 with ∑wj=1. Suppose that the each factor (S,O,D) is denoted cij (Sij , Oij , Dij). Then
C=[cij]m×n is a fuzzy decision matrix. In Fig 1,cij is expressed in an interval-value TFN:
1 2 3
1 2 3
, ,
(3)
, ,
a a a
C
a a a
=
Then, C=[(a1,a’1);a2;(a’3,a3)]. The normalized decision matrix R can thus be calculated. Given
Cij=[(a1,a’1);a2;(a’3,a3)], the normalized performance rating is :
' '
[( , ); ;( , )] , 1,2,..., ;
1,2,..., (4)
ij ij ij ij ij
ij
j j j j j
a a b a a
r i m
d d d d d
j n for j I
+ + + + +
= =
= ∈
' '
[( , ); ;( , )] , 1,2,..., ;
1,2,..., (5)
j j j j j
ij
ij ij ij ij ij
a a a a a
r i m
d d b a a
j n for j J
− − − − −
= =
= ∈
Where d+
j=max{cij,i=1,…..,m},and a’
j=min{aij,i=1,…. ..,m}. Given that rij=[(lij,l’
ij);mij;(uij,u’
ij)],
R=[rij]m×n ,can be obtained , and R0=(r01,r02,…….,r0n)=([(1,1);1(1,1)],[(1,1); 1
;(1,1)],…….,[(1,1);1;(1,1)]).
1
1
2 1
2 1
3
2 3
3 2
0,
.(1)
0,
a
x a
x a
a x a
a a
Eq
a x
a x a
a a
otherwise
µ
<
−
≥ ≥
−
=
− ≥ ≥
−
5. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
11
Fig 1. An interval-valued TFN
The distance between the reference value and each comparison value can be calculated using
definition (2):
(1) ' 2 2 ' 2
(2) 2 2 2
1
[( 1) ( 1) ( 1) ] (6)
3
1
[( 1) ( 1) ( 1) ]
3
ij ij ij ij
ij ij ij ij
l m u
l m u
δ
δ
= − + − + −
= − + − + −
This calculation is used to determine the distance between the reference value and the comparison
value in the interval δij= [δij
(1)
,δij
(2)
].
Hence this study uses a formula to determine the factor weight (Zhnag et al.2011[13])
(1) (2)
1
(1) (2)
1 1
( )
(7)
( )
m
ij ij
i
j m n
ij ij
i i
w
δ δ
δ δ
=
= =
+
=
+
∑
∑∑
The weight vector of the criteria is applied to decision matrix A. The reference series and the
comparison series constitute the interval value δij= [δij
(1)
,δij
(2)
]. The concept of a linguistic
preference is useful to address uncertainties, i.e. for description in conventional linguistic
expression table 2 indicates how the interval-valued triangular fuzzy membership function can
accommodate the qualitative data while the evaluators process the evaluation in the form of
linguistic information.
2.3. Prospect theory
The value function used in the prospect theory is described in form of a power law expressed as:
6. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
12
0
( ) (8)
( ) 0
x if x
v x
x if x
α
β
θ
≥
=
− − <
Where α and β are parameters related to gains and losses, respectively. The parameter θ
represents a characteristic that is steeper for losses than for gains when considering cases for
which risk aversion θ>1. Fig 2
Fig 2. Value function of the TODIM method.
2.4. TODIM
The TODIM method uses paired comparison between the factors by using technically simple
resource to eliminate occasional inconsistencies resulting from these comparisons. TODIM
allows value judgments to be performed on a verbal scale using a criteria hierarchy, fuzzy value
judgments and interdependence relationships among the alternatives. The alternatives (potential
risk) (A1,A2,…,Am) are viable alternatives,c1, c2,c3 are represented factors, and xij indicates the
rating of alternative Aij according to the criteria cj. The weight vector w= (w1,w2,…wn) comprises
the individual weights wj(j=1,…n) for each criterion cj satisfying ∑n
i=1 wj=1. The data of the
decision matrix A originate from different sources. The matrix is required to normalize it to
transform it into a dimensionless matrix and allows various criteria to be compared. This study
use the normalized decision matrix R=[rij]m×nwith i=1,…,m and j=1,…,n. M.-L. Tseng et
al.(2012) [14]
11 1
1
(9)
n
m mn
x x
A
x x
=
K
M O M
L
TODIM then calculates the partial dominance matrices and the final dominance matrix. The first
calculation that decision makers must define is a reference criterion (typically the criterion with
7. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
13
the greatest importance weight). Therefore, wrc indicates the weight of the criterion c by the
reference criteria r. TODIM is expressed by the following equations. The dominance of each
alternative over each alternative is:
( , )
1
( , ) ( , ) (10)
m
i j c i j i j
c
A A A Aδ φ ∀
=
= ∑
Where
1
1
( )
( ) 0
( , ) 0 ( ) 0 (11)
( )( )
1
( ) 0
rc ic jc
ic jcm
rc
c
i j ic jc
m
rc ic jc
c
ic jc
rc
w x x
if x x
w
A A if x x
w x x
if x x
w
φ
θ
=
=
−
− >
= − =
−
−
− <
∑
∑
The term φc(Ai,Aj) represents the contribution of criterion c (c=1,…, m) to the function δ(Ai,Aj)
when comparing alternative i with alternative j. The parameter θ represents the attenuation factor
of the losses, whose mitigation depends on a specific problem. A positive (xic-xjc) represents a
gain. Whereas a nil or a negative (xic-xjc) represents a loss. The final matrix of dominance is
obtained by summing the partial matrices of dominance for each criterion. The global value of the
alternative I is determined by normalizing the final matrix of dominance according the following
expression: ∑δ(i,j)
1 1
1 1
( , ) min ( , )
(12)
max ( , ) min ( , )
n n
j j
i n n
j j
i j i j
i j i j
δ δ
ξ
δ δ
= =
= =
−
=
−
∑ ∑
∑ ∑
Ordering the values ξi provides the rank of each alternative, and better alternatives have higher
values of ξi .Use of numerical values in rating alternatives may be limited in their capacity to
address uncertainties. Therefore, an extension of TODIM is proposed to solve problems with
decision making with uncertain data resulting in fuzzy TODIM. In practical applications, the
triangular shape of the membership function is often used to represent fuzzy numbers. Fuzzy
models using TFNs proved highly effective for solving decision making problems for which the
available information is imprecise. Hence, this study provides some basic definitions of fuzzy set
theory.
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3.2. Fuzzy time function
A fuzzy time functionconsists of three functions for each way, for example when we are
optimistic about some criteria we predict the situation in the best possible way, we could produce
a function with collecting the opinion of decision makers, and for normal and pessimistic we do
the same thing. It is necessary for the function to be parallel because it is not logicthatthese three
functions cut themselves.Fig1
For example:
Customer satisfaction on green supply products:
We have some methodsthat can be used for these criteria to satisfy the customer requirements,
each of method can be doing some good in the period of time, and in the other period it can’t be a
good method.
Fig1-Method in different time has different effect
In the fact, this function in each time represents fuzzy triangular number, which is considering all
three possibilities. Mahmoodi&Arshadi(2014)[14]
Why using FTF?
In many organizations some methods or some equipment could be pass the cycle life or the new
equipment or method are better than the older ones. With FTF we could consider these things to
our decisions and we could use the data of today for tomorrow and upgrade data if it was
necessary. In fact the first decision can be a principle of the future decisions.
Mahmoodi&Arshadi(2014)[15]
0
2
4
6
8
10 20 30 40
Customer
satisfaction
method A
upper
bound
9. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
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1
1 2
3
1
optimistic
( ) (2)
pessimistic
*
1
F for
FTF c F for normal
F for
F funciton for optimistic
opinion during thetime for criteria
=
=
According Eq.2 in the fact FTF represent the triangular fuzzy number during the time.
1 2 3 1 2 3( , , ) ( , , ) (3)A a a a FTF F F F= → =
2.5. Proposed approach
This study attempts to apply fuzzy set theory and TODIM for ranking the risk of eight
alternatives with fuzzy FMEA approach. The goal is to analyze how proposed method can be
used to determine the risk factors of FMEA against alternative.
Step 1.A group of decision makers identifies the failure modes.
Step 2.Interpret the linguistic preference for the interval-valued TFNs. Use linguistic preference
to convert the interval-valued TFNs into crisp value then perform fuzzy assessments according
the Eqs (3)-(6) to remove the fuzziness and to aggregate the measures into a crisp value (Wj).
Step 3.Use Eq. (7) to determine the initial interval-valued TFNs decision matrix A. The term φc=
(Ai,Aj) represents the contribution of the criterion c to the function δ (Ai,Aj) when comparing
alternative I with alternative j using Eqs. (10) and (11). The final matrix of dominance is obtained
by summing the partial matrices of dominance for each criterion.
Step4. Using the FTF for evaluating risk in different times, helped us to find out about the future
failure of our system .we can do this in two ways. One is evaluating risk bycollecting data from
expert’s and their opinion about how will be thechange of each criteria in thefuture or by using
one function for each alternative to represent all effects of criteria.
Step 5.Calculate the global value of the alternatives by normalizing the final matrix dominance
using Eq. (12). Ordering the values ξi provides the rank of each alternative. Important
alternativesare those that have the highest ξi. The function φc= (Ai,Aj) permits the data to be
adjusted to prospect theory’s value function. Fig (3).
Step6.combining the results of step 4 and step 5 to reach final table which represent weight of
alternatives and criteria in different times.
Step 7. Using fuzzy time function for period of time needed in our research our managers need to
know about the situation of criteria(FMEA factors) and alternatives in their organization.
10. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
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Failure determination
Experts
Experts
Data collection for
evalution failure modes
with respect to risk
factors
Fuzzy TODIM
Closseness
coefficitnets and
ranking
Fuzzy time
function
Fig 3. Flowchart of fuzzy FMEA
3. AN ILLUSTRATIVE EXAMPLE
The proposed methodology is applied to manufacturing facility of a SME performing in an
automotive industry. Major potential failure modes ( PFMs) are identified by a group of experts
in an assembly process at the manufacturing facility as non-conforming material (A), wrong die
(B), wrong program (C). Excessive cycle time (D), wrong process (E), damaged goods (F), wrong
part (G), and incorrect forms (H).
3.1. Results
This study evaluates the eight alternatives which have priority risk. First we must find out the
weight of risk factors, and then find out about the alternative weights. With ranking the
alternative the priority risk will be revealed. Expert opinion can has weight. For example some
expert’s opinion might be more important than others. In this study we supposed all expert’s
opinions are the same .we also research about the changing weight of criteria in the 10 and 20
months after this evaluation and will consider how much time this evaluation will be effective in
our process with other hands we actually determine the life of alternatives.
11. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
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Step1. Table 3 presents the qualitative scales that require translation into interval-valued TFNs
(see Table 2).
Step2. Table 4 present interval-valued TFNs, and the defuzzification process is employed in Eq.
(7). The TFNs were applied to transform the total weighed matrices into interval performance
matrices. The linguistic preferences were used to convert measures into a crisp value (Wj), Shown
in Table 1. The TFNs were converted into crisp values shown in Table 6.
Step3. The risk factors weight is calculate from Eq. (7) is shown in Table 5. Step4. Using Eq. (9)
to determine the initial interval valued TFNs decision matrix, the computations demonstrate how
to determine the dominance measurements (A, B), which are presented. The computations
represent the values of the measurements of dominance after the implementation of the
mathematical formulation of the fuzzy TODIM method.
Step5. Eq. (10) determines the values of the dominance measures, and δ (A, B) is obtained for the
different values of φ (A,B) for all factors. The following computational processes are determined
using Eq. (11). (Table 7
Step6. Eq (12) calculates the overall value of the alternatives by normalizing the corresponding
dominance measurements. The rank of each alternative derives from ordering the alternative
respective values. The global measures computed the complete rank ordering of all alternatives.
In addition, a sensitivity analysis should then be applied to verify the stability of result based on
the decision maker’s preferences. The results are presented in Table 8.
Table3.Evalution of experts in linguistic variable for risk factor against PFMS.
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Table 4.Interval-valued TFNS decision matrix.
Table 5. Factors (RPN)weight
Table 6. Matrix of Alternative score respect FMEA factors
Table 7.following computational processes Eq(11)
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1 1
1 1
( , ) min ( , )
4.025 0.994
3.031
0.07 0.994
max ( , ) min ( , )
n n
j j
i n n
j j
i j i j
i j i j
δ δ
ξ
δ δ
= =
= =
−
− +
= = = −
+
−
∑ ∑
∑ ∑
Table 8.Final weights of Alternatives
Step7. The table 8 represents the weight of each criteria at present time but If we want to know in
10 or 20 month later which of this criteria have more RPN in our system what should we do? In
here we use FTF for each of these 8 criteria. For example the company policy after this
evaluation is reduce risk of first three criteria with weight of 0.3 and for others will be divided
(0.1/5) but it’s not all the way through because we must consider time effect to this alternative
and how they will be change. For this kind of things we use fuzzy time function which helps us to
consider all situations it might happen in future.
For example we do this for criteria Numbers in table 9 are represent the severity of failure modes
in 5, 10, 15,Month.in last column it’s empty and it’s means in which time this criteria will be
removed from our system.0.1t is function represent the normal increasing of this criteria during
time which collected from experts. After 50 month of this research in organization, if with
activities goes with this rate the failure E will self remove from the system. In this example we
just suppose it’s 0.1t.
0.1 0.3 7.68 0 15
( ) 0.1 0.3 0.5 7.68 15,
0.1 0.3 7.18 15
e
t t t
y t t t t t
t t t
t per month
− + ≤ <
= − + + =
− + < < ∞
=
14. International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.2, April 2014
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Table 9. The rate of RPN in of alternative E .
This numbers means in 15 month after this evaluation with policy of company will be reduced
but in 20 month because of coming new technology to system this criteria will be increase and the
cause of that it’s the cost of be familiar to new technology. And with this sequence after 10 month
will be reduced to poor and this sequence will help us to forecast other periods and ending time.
( ) 0.1 0.3 7.18 15 35.9 35.9 15 50.9ey t t t t t= − + < < ∞ ⇒ = ⇒ + =
Finally we can find out this criteria when will be removed effectively. This can be done for every
criterion depend on time.
4. CONCLUSION
FMEA, designed to provide information for risk management decision –making, is a widely used
engineering techniquein industries. With TODIM approach decision makers can find out about
any loss and gain between alternatives. For example in Table 7 ,we can find out the alternative A
against B have -0.447 in factor severity ,this means the severity of A is more critical than severity
of B ,but the in occurrence , occurrence of B is more critical than B. this represent a great view of
system for decision makers. In TODIM, it’s easier to find out about the relationship between
alternatives in each factor, but in the other solution like Fuzzy TOPSIS we can’t say the same
thing.
The other aspect of this study is using FTF in the way of forecasting the future of the criteria
which is very important for each firm to know when and where they most spends them money,
which this work is done in supplier selection in green supply chain management. It will be
suggested using fuzzy time function in other studies for predicting efficiency of system.
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