Fuzzy Set Theory—and Its ApplicationsFuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included. |
Contents
| 6 | |
Extensions | 23 |
4 | 41 |
1 | 53 |
Fuzzy Relations and Fuzzy Graphs | 69 |
Fuzzy Analysis | 91 |
Possibility Theory Probability Theory and Fuzzy | 109 |
Applications of Fuzzy Set Theory | 127 |
Fuzzy Control | 203 |
Fuzzy Data Analysis | 241 |
Decision Making in Fuzzy Environments | 281 |
38 | 308 |
Fuzzy Set Models in Operations Research | 321 |
53 | 342 |
Empirical Research in Fuzzy Set Theory | 369 |
Future Perspectives | 403 |
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Common terms and phrases
aggregation algorithm applications of fuzzy approach areas assignment Bezdek classical compute concepts considered constraints control action crisp criteria data analysis decision maker defined definition defuzzification degree of membership denotes described determined domain Dubois and Prade example expert systems formal Fril fuzzy clustering fuzzy control fuzzy control systems fuzzy event fuzzy function fuzzy graph fuzzy logic fuzzy numbers fuzzy relation fuzzy set decision fuzzy set theory goal heuristic inference input integral interpreted intersection interval linear programming linguistic variable Mamdani mathematical matrix maximize membership function methods min-operator objective function operations research optimal parameters partition possibility distribution possibility theory probability probability theory problem proposition R₁ representing respect rules schedule semantic shown in figure solution structure Sugeno t-norms temperature true truth tables truth values uncertainty x₁ Yager Zadeh Zimmermann µÃ(x µğ(x µµ(x