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
Page x
... degree of achievement " . 217 Figure 10-10 Figure 10-11 Figure 10-12 Figure 11-1 Figure 11-2 Generic Mamdani fuzzy ... membership functions . 236 Figure 11-8 Separate membership functions . 236 Figure 11-9 Figure 11-10 Parameters ...
... degree of achievement " . 217 Figure 10-10 Figure 10-11 Figure 10-12 Figure 11-1 Figure 11-2 Generic Mamdani fuzzy ... membership functions . 236 Figure 11-8 Separate membership functions . 236 Figure 11-9 Figure 11-10 Parameters ...
Page 7
... degree usually either via linguistic vari- ables or via fuzzy data analysis ( fuzzy clustering etc. ) . d ) Meaning ... membership functions of fuzzy sets , which can then be retranslated into words and sentences via linguistic ...
... degree usually either via linguistic vari- ables or via fuzzy data analysis ( fuzzy clustering etc. ) . d ) Meaning ... membership functions of fuzzy sets , which can then be retranslated into words and sentences via linguistic ...
Page 12
... membership function or grade of membership ( also degree of compatibility or degree of truth ) of x in A that maps X to the membership space M ( When M contains only the two points 0 and 1 , A is nonfuzzy and μà ( x ) is identical to ...
... membership function or grade of membership ( also degree of compatibility or degree of truth ) of x in A that maps X to the membership space M ( When M contains only the two points 0 and 1 , A is nonfuzzy and μà ( x ) is identical to ...
Page 13
... membership function is not limited to values between 0 and 1. If sup ̧μà ( x ) = 1 , the fuzzy set à is called ... degree of membership zero . Often it is appropriate to consider those elements of the universe that have a nonzero degree ...
... membership function is not limited to values between 0 and 1. If sup ̧μà ( x ) = 1 , the fuzzy set à is called ... degree of membership zero . Often it is appropriate to consider those elements of the universe that have a nonzero degree ...
Page 14
... degree a is called the a - level set : A = { x = X | u ( x ) 20 } Aά = { x = X | μà ( x ) > α } is called " strong a ... membership function rather than the support of the fuzzy set . Definition 2-4 A fuzzy set à is convex if μà ( λx1 + ...
... degree a is called the a - level set : A = { x = X | u ( x ) 20 } Aά = { x = X | μà ( x ) > α } is called " strong a ... membership function rather than the support of the fuzzy set . Definition 2-4 A fuzzy set à is convex if μà ( λx1 + ...
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 à 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 µÃ(x µµ(x