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 viii
... Function 342 14.3 Fuzzy Dynamic Programming 348 14.3.1 Fuzzy Dynamic Programming with Crisp State Transformation ... Membership Functions 453 16.2.1 Type A - Membership Model 454 16.2.2 Type B - Membership Model 456 16.3 Empirical ...
... Function 342 14.3 Fuzzy Dynamic Programming 348 14.3.1 Fuzzy Dynamic Programming with Crisp State Transformation ... Membership Functions 453 16.2.1 Type A - Membership Model 454 16.2.2 Type B - Membership Model 456 16.3 Empirical ...
Page xi
... function f ( t ) and the resulting pointwise similarity μ ( f ( t ) ) ; ( b ) projection of pointwise similarity into the plane ( t , μ ( f ... Membership functions resulting from incremental classifier design and LIST OF FIGURES xi.
... function f ( t ) and the resulting pointwise similarity μ ( f ( t ) ) ; ( b ) projection of pointwise similarity into the plane ( t , μ ( f ... Membership functions resulting from incremental classifier design and LIST OF FIGURES xi.
Page xii
Hans-Jürgen Zimmermann. Figure 15-5 Membership functions resulting from incremental classifier design and ... function of the fuzzy goal G. Figure 15-16 The solution of the numerical example . 384 385 386 386 387 388 388 392 392 394 ...
Hans-Jürgen Zimmermann. Figure 15-5 Membership functions resulting from incremental classifier design and ... function of the fuzzy goal G. Figure 15-16 The solution of the numerical example . 384 385 386 386 387 388 388 392 392 394 ...
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 μĆ ( 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 μĆ ( x ) is identical to ...
Page 13
... membership function is not limited to values between 0 and 1. If sup ̧μĆ ( x ) = 1 , the fuzzy set Ć is called ... function a generalization of the characteristic function . Since we are gener- ally referring to a universal ( crisp ) ...
... membership function is not limited to values between 0 and 1. If sup ̧μĆ ( x ) = 1 , the fuzzy set Ć is called ... function a generalization of the characteristic function . Since we are gener- ally referring to a universal ( crisp ) ...
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