Fuzzy Set Theory—and Its ApplicationsSince its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have been made in many directions. The primary goal of Fuzzy Set Theory - and its Applications, Fourth Edition is to provide a textbook for courses in fuzzy set theory, and a book that can be used as an introduction. To balance the character of a textbook with the dynamic nature of this research, many useful references have been added to develop a deeper understanding for the interested reader. Fuzzy Set Theory - and its Applications, Fourth Edition updates the research agenda 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. Chapters have been updated and extended exercises are included. |
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Page v
... Fuzzy Sets Crispness , Vagueness , Fuzziness , Uncertainty Fuzzy Set Theory ix xiii XV xvii xix 112 2 Part I : Fuzzy Mathematics 9 22 Fuzzy Sets - Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set - Theoretic Operations for Fuzzy ...
... Fuzzy Sets Crispness , Vagueness , Fuzziness , Uncertainty Fuzzy Set Theory ix xiii XV xvii xix 112 2 Part I : Fuzzy Mathematics 9 22 Fuzzy Sets - Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set - Theoretic Operations for Fuzzy ...
Page vi
Hans-Jürgen Zimmermann. 6 6.1 6.1.1 6.1.2 6.2 Fuzzy Relations and Fuzzy Graphs Fuzzy Relations on Sets and Fuzzy Sets Compositions of Fuzzy Relations Properties of the Min - Max Composition Fuzzy Graphs 6.3 Special Fuzzy Relations 7 Fuzzy ...
Hans-Jürgen Zimmermann. 6 6.1 6.1.1 6.1.2 6.2 Fuzzy Relations and Fuzzy Graphs Fuzzy Relations on Sets and Fuzzy Sets Compositions of Fuzzy Relations Properties of the Min - Max Composition Fuzzy Graphs 6.3 Special Fuzzy Relations 7 Fuzzy ...
Page viii
Hans-Jürgen Zimmermann. 14 Decision Making in Fuzzy Environments 329 14.1 Fuzzy ... Set Models in Logistics 15.3.2.2 Fuzzy Linear Programming in Logistics 15.3 ... Theory 443 16.1 Formal Theories vs. Factual Theories vs. Decision Technologies ...
Hans-Jürgen Zimmermann. 14 Decision Making in Fuzzy Environments 329 14.1 Fuzzy ... Set Models in Logistics 15.3.2.2 Fuzzy Linear Programming in Logistics 15.3 ... Theory 443 16.1 Formal Theories vs. Factual Theories vs. Decision Technologies ...
Page xi
... theoretic clusters . 285 Figure 13-7 The butterfly . 286 Figure 13-8 Crisp ... set ; ( b ) circles found by FSC ; ( c ) data set ; ( d ) circles found by ... fuzzy set " approximately zero " ( μ ( y ) ) , the function f ( t ) and the ...
... theoretic clusters . 285 Figure 13-7 The butterfly . 286 Figure 13-8 Crisp ... set ; ( b ) circles found by FSC ; ( c ) data set ; ( d ) circles found by ... fuzzy set " approximately zero " ( μ ( y ) ) , the function f ( t ) and the ...
Page xvii
Hans-Jürgen Zimmermann. Since its inception 20 years ago , the theory of fuzzy sets has advanced in a variety of ways and in many disciplines . Applications of this theory can be found , for example , in artificial intelligence ...
Hans-Jürgen Zimmermann. Since its inception 20 years ago , the theory of fuzzy sets has advanced in a variety of ways and in many disciplines . Applications of this theory can be found , for example , in artificial intelligence ...
Contents
1 | |
8 | |
22 | |
4 | 44 |
The Extension Principle and Applications | 54 |
Fuzzy Relations on Sets and Fuzzy Sets | 71 |
3 | 82 |
7 | 88 |
Applications of Fuzzy Set Theory | 139 |
3 | 154 |
4 | 160 |
5 | 169 |
Fuzzy Sets and Expert Systems | 185 |
Fuzzy Control | 223 |
Fuzzy Data Bases and Queries | 265 |
Decision Making in Fuzzy Environments | 329 |
3 | 95 |
4 | 105 |
2 | 122 |
4 | 131 |
Applications of Fuzzy Sets in Engineering and Management | 371 |
Empirical Research in Fuzzy Set Theory | 443 |
Future Perspectives | 477 |
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Common terms and phrases
a-level aggregation algebraic algorithm applications of fuzzy approach approximately areas base basic Bezdek chapter classical computational concepts considered constraints crisp criteria customers data analysis DataEngine decision defined definition defuzzification degree of membership described determine domain Dubois and Prade elements engineering example expert systems feature formal Fril fuzzy c-means fuzzy clustering fuzzy control fuzzy control systems fuzzy function fuzzy graph fuzzy logic fuzzy measures fuzzy numbers fuzzy relation fuzzy set Ć fuzzy set theory goal inference inference engine input integral intersection interval linear programming linguistic variable Mamdani mathematical measure of fuzziness membership function methods min-operator objective function operators optimal parameters possibility distribution probability probability theory problem properties respect rules scale level scheduling semantic solution structure Sugeno t-conorms t-norms Table tion trajectories truth tables truth values uncertainty vector x₁ Yager Zadeh Zimmermann µĆ(x µµ(x