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. |
From inside the book
Results 1-5 of 12
Page ix
... t - norms , t - conorms , and averaging operators . Figure 5-1 The extension principle . Figure 5-2 Trapezoidal " fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 ...
... t - norms , t - conorms , and averaging operators . Figure 5-1 The extension principle . Figure 5-2 Trapezoidal " fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 ...
Page 29
... conorms- and the class of averaging operators , which model connectives for fuzzy sets between t - norms and t - conorms . Each class contains parameterized as well as nonparameterized operators . t - norms . T - norms were initiated in ...
... conorms- and the class of averaging operators , which model connectives for fuzzy sets between t - norms and t - conorms . Each class contains parameterized as well as nonparameterized operators . t - norms . T - norms were initiated in ...
Page 30
... t - norms as they are used today . The mathematical aspects of t - norms are excellently presented in the book by Klement , Mesiar and Pap [ Klement et al . 2000 ] . The use of t - norms and t - conorms for modeling the intersection and ...
... t - norms as they are used today . The mathematical aspects of t - norms are excellently presented in the book by Klement , Mesiar and Pap [ Klement et al . 2000 ] . The use of t - norms and t - conorms for modeling the intersection and ...
Page 31
... t - conorms or s - norms are associative , commutative , and monotonic two - placed functions s that map from [ 0 ... t - norms and t - conorms are related in a sense of logical duality . Alsina [ Alsina 1985 ] defined a t - conorm ...
... t - conorms or s - norms are associative , commutative , and monotonic two - placed functions s that map from [ 0 ... t - norms and t - conorms are related in a sense of logical duality . Alsina [ Alsina 1985 ] defined a t - conorm ...
Page 32
... t - conorm is bounded by the max - operator and the operators , respectively [ Dubois and Prade 1982a , p . 42 ] ... conorms , often main- taining the associativity property . For illustration purposes , we review some interesting ...
... t - conorm is bounded by the max - operator and the operators , respectively [ Dubois and Prade 1982a , p . 42 ] ... conorms , often main- taining the associativity property . For illustration purposes , we review some interesting ...
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