Fuzzy soft set theory
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The document discusses using fuzzy soft set approaches combined with Dempster–Shafer theory of evidence and grey relational analysis for decision making under uncertainty. Grey relational analysis is used to obtain the uncertain degrees of parameters. Mass functions are assigned to choices based on the uncertain degrees. Dempster's rule of evidence is used to combine choices into a collective choice. This approach avoids selecting soft set levels and parameter weights while improving reliability and the level of decision making.
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This document discusses the debate between qualitative and quantitative research methods and argues that mixed methods research provides a solution. It provides advantages and disadvantages of both qualitative and quantitative research. Mixed methods allows researchers to gain a more comprehensive understanding by combining both approaches. Using multiple research methods offsets the weaknesses of individual methods.
httphome.ubalt.eduntsbarshbusiness-statoprepartIX.htmTool.docx
http://home.ubalt.edu/ntsbarsh/business-stat/opre/partIX.htm
Tools for Decision Analysis: Analysis of Risky Decisions
If you will begin with certainties, you shall end in doubts, but if you will content to begin with doubts, you shall end in almost certainties. -- Francis Bacon
Making decisions is certainly the most important task of a manager and it is often a very difficult one. This site offers a decision making procedure for solving complex problems step by step.It presents the decision-analysis process for both public and private decision-making, using different decision criteria, different types of information, and information of varying quality. It describes the elements in the analysis of decision alternatives and choices, as well as the goals and objectives that guide decision-making. The key issues related to a decision-maker's preferences regarding alternatives, criteria for choice, and choice modes, together with the risk assessment tools are also presented.
Professor Hossein Arsham
MENU
1. Introduction & Summary
2. Probabilistic Modeling: From Data to a Decisive Knowledge
3. Decision Analysis: Making Justifiable, Defensible Decisions
4. Elements of Decision Analysis Models
5. Decision Making Under Pure Uncertainty: Materials are presented in the context of Financial Portfolio Selections.
6. Limitations of Decision Making under Pure Uncertainty
7. Coping with Uncertainties
8. Decision Making Under Risk: Presentation is in the context of Financial Portfolio Selections under risk.
9. Making a Better Decision by Buying Reliable Information: Applications are drawn from Marketing a New Product.
10. Decision Tree and Influence Diagram
11. Why Managers Seek the Advice From Consulting Firms
12. Revising Your Expectation and its Risk
13. Determination of the Decision-Maker's Utility
14. Utility Function Representations with Applications
15. A Classification of Decision Maker's Relative Attitudes Toward Risk and Its Impact
16. The Discovery and Management of Losses
17. Risk: The Four Letters Word
18. Decision's Factors-Prioritization & Stability Analysis
19. Optimal Decision Making Process
20. JavaScript E-labs Learning Objects
21. A Critical Panoramic View of Classical Decision Analysis
22. Exercise Your Knowledge to Enhance What You Have Learned (PDF)
23. Appendex: A Collection of Keywords and Phrases
Companion Sites:
· Business Statistics
· Success Science
· Leadership Decision Making
· Linear Programming (LP) and Goal-Seeking Strategy
· Linear Optimization Software to Download
· Artificial-variable Free LP
Solution
Algorithms
· Integer Optimization and the Network Models
· Tools for LP Modeling Validation
· The Classical Simplex Method
· Zero-Sum Games with Applications
· Computer-assisted Learning Concepts and Techniques
· Linear Algebra and LP Connections
· From Linear to Nonlinear Optimization with Business Applications
· Construction of the Sensitivity Region for LP Models
· Zero Sagas in Four Dimensions
· Systems Simulation
· B.
Prediciting happiness from mobile app survey data
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Advanced Statistical Methods in Meta-analysis Enhancing Accuracy, Reliability...
Meta-analysis is a powerful statistical method that combines the results of multiple studies to provide more reliable estimates of the effects of various interventions or treatments. If you're looking for expert meta-analysis services in the pharmaceutical industry, Pubrica is here to help.
Advanced Statistical Methods in Meta-analysis Enhancing Accuracy, Reliability...
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Multivariate Approaches in Nursing Research Assignment.pdf
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Fuzzy soft set theory
- 2. Fuzzy soft set approach in decision making plays a crucial role by using Dempster–Shafer theory of evidence. First, the uncertain degrees of several parameters are obtained via grey relational analysis that apply to calculate the grey mean relational degree. Secondly, a mass functions of different independent choices with several parameters have given according to the uncertain degree. Lastly, aggregate the choices into a collective choices, Dempster’s rule of evidence combination have been utilized. The aforesaid soft computing based method have been applied on decision making problem.
- 3. To solve complicated problems in economics, engineering, environmental science and social science, classical mathematical methods are not always successful because of various types of uncertainties present in these problems. There are several theories: probability theory, fuzzy set theory, rough set theory and interval mathematics which we can consider as mathematical tools for dealing with uncertainties. But all these theories have their own complications to solve the decision making problem. To overcome these kinds of complications, soft set theory for modeling uncertainty have been introduced. Recently works on soft set theory are developing promptly. The combination of fuzzy set and soft sets popularly referred to as fuzzy soft sets theory is also known as a degree attached with the parameterization of fuzzy sets while defining a fuzzy soft set.
- 4. The study of hybrid models combining soft sets or fuzzy soft sets with other mathematical structures and new operations are emerging as an active research topic of soft set theory. Compared to probability theory, Dempster– Shafer theory of evidence can capture more information to support decision-making by identifying the uncertain and unknown evidence. It provides a mechanism to derive solutions from various vague evidences without knowing much prior information and has been successfully applied into many fields such as intelligent medical diagnosis, knowledge reduction, fault diagnosis, multi-class classification, supplier selection in managerial approach etc. Furthermore, applying both theories enables the eventual decision makers to take advantage of both methods merits and make evaluation experts to treaty with uncertainty and risk assertively
- 5. The hybrid model has been demonstrated to have its practicality and flexibility in successfully solving an assortment of problems in the information sciences, such as data mining, knowledge discovery, and decision making. Therefore, it is very meaningful to discover an approach to fuzzy soft set in decision making by combining Dempster–Shafer theory of evidence with grey relational analysis. The fuzzy soft set approach in decision making based on grey relational analysis and Dempster– Shafer theory of evidence. The novelty aspects or advantages of this approach is avoiding the selection of appropriate level soft sets and distribution of parameters’ weight, reducing significantly the uncertainty of decision- making and the fuzziness of people’s subjective understanding, improving the reliability of decision making and increasing the level of decision-making.
- 6. Compared to probability theory, Dempster–Shafer theory of evidence captures more information to support decision making, by recognizing the uncertain and unknown evidences. It provides a apparatus to derive solutions from various vague evidences (or parameter) without knowing much prior information. From mass functions of choices with each evidence (or parameter) earlier if we apply Dempster–Shafer theory of evidence to make decisions. However, how to find uncertain degree of evidences (or parameters) is a critical problem. Grey relational analysis is employed as a means to reflect uncertainty between experts in multiple parameter models through the membership value. Next, we apply grey relational analysis to obtain uncertain degree of evidences (or parameters).