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 ix
... 2 Linguistic variable “ Probability ” . 144 Figure 9-3 Linguistic variable " Truth " . 145 Figure 9-4 Terms " True " and " False " . 146 Figure 10-1 Structure of an expert system . 189 Figure List of Figures 1 2 List of Figures 6 1 1 2 2.
... 2 Linguistic variable “ Probability ” . 144 Figure 9-3 Linguistic variable " Truth " . 145 Figure 9-4 Terms " True " and " False " . 146 Figure 10-1 Structure of an expert system . 189 Figure List of Figures 1 2 List of Figures 6 1 1 2 2.
Page xxiii
... true , in spite of the fact , that evolu- tionary computing has its strength in optimization , neural nets are particularly strong in pattern recognition and automatic learning , whereas fuzzy set theory has its strength in modeling ...
... true , in spite of the fact , that evolu- tionary computing has its strength in optimization , neural nets are particularly strong in pattern recognition and automatic learning , whereas fuzzy set theory has its strength in modeling ...
Page 1
... true or false — and nothing in between . In set theory , an element can either belong to a set or not ; and in optimization , a solution is either feasible or not . Precision assumes that the parameters of a model represent exactly ...
... true or false — and nothing in between . In set theory , an element can either belong to a set or not ; and in optimization , a solution is either feasible or not . Precision assumes that the parameters of a model represent exactly ...
Page 7
... true or false ) rather than knowledge processing . In approximate reasoning meanings are attached to words and sentences via lin- guistic variables . Inference engines then have to be able to process meaningful linguistic expressions ...
... true or false ) rather than knowledge processing . In approximate reasoning meanings are attached to words and sentences via lin- guistic variables . Inference engines then have to be able to process meaningful linguistic expressions ...
Page 8
... true if one considers the inaccuracies and uncertainties contained in the input data . It seems desirable that an introductory textbook be available to help students get started and find their way around . Obviously , such a textbook ...
... true if one considers the inaccuracies and uncertainties contained in the input data . It seems desirable that an introductory textbook be available to help students get started and find their way around . Obviously , such a textbook ...
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