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 83
Page xi
... values for variable " elements ' rigidity " . Linguistic values for variable " significance " . Linguistic evaluation values of lathes B , C , D , E. 377 379 380 Figure 15-5 Membership functions resulting from incremental classifier ...
... values for variable " elements ' rigidity " . Linguistic values for variable " significance " . Linguistic evaluation values of lathes B , C , D , E. 377 379 380 Figure 15-5 Membership functions resulting from incremental classifier ...
Page 1
... values or their occurrence . If the model under consideration is a formal model [ Zimmermann 1980 , p . 127 ] , that is , if it does not pretend to model reality ade- quately , then the model assumptions are in a sense arbitrary , that ...
... values or their occurrence . If the model under consideration is a formal model [ Zimmermann 1980 , p . 127 ] , that is , if it does not pretend to model reality ade- quately , then the model assumptions are in a sense arbitrary , that ...
Page 7
... values 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 ...
... values 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 ...
Page 13
... values between 0 and 1. If sup ̧μĆ ( x ) = 1 , the fuzzy set Ć is called normal . A non- empty fuzzy set A can always be normalized by dividing μ ( x ) by supμ ( x ) : As a matter of convenience , we will generally assume that fuzzy ...
... values between 0 and 1. If sup ̧μĆ ( x ) = 1 , the fuzzy set Ć is called normal . A non- empty fuzzy set A can always be normalized by dividing μ ( x ) by supμ ( x ) : As a matter of convenience , we will generally assume that fuzzy ...
Page 18
... justification of specific mathematical models . We shall therefore sketch their reasoning : Consider two statements , S and T , for which the truth values are μs and μr , respectively , μs , HT E 18 FUZZY SET THEORY - AND ITS APPLICATIONS.
... justification of specific mathematical models . We shall therefore sketch their reasoning : Consider two statements , S and T , for which the truth values are μs and μr , respectively , μs , HT E 18 FUZZY SET THEORY - AND ITS APPLICATIONS.
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 |
Other editions - View all
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