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 6-10 of 68
Page xxiii
... uncertainties . Particularly between fuzzy set theory and neural nets the synergies have been used to develop hybrid models and methods , that combine the strengths of both of these areas . Nevertheless , all three areas are continuing ...
... uncertainties . Particularly between fuzzy set theory and neural nets the synergies have been used to develop hybrid models and methods , that combine the strengths of both of these areas . Nevertheless , all three areas are continuing ...
Page xxv
... uncertainty modeling because I am convinced that chapters 2 to 7 are still sufficient as a mathematical basis to under- stand all new developments in this area and also for part II of the book , where the major changes and extensions of ...
... uncertainty modeling because I am convinced that chapters 2 to 7 are still sufficient as a mathematical basis to under- stand all new developments in this area and also for part II of the book , where the major changes and extensions of ...
Page 1
... Uncertainty Most of our traditional tools for formal modeling , reasoning , and computing are crisp , deterministic , and precise in character . By crisp we mean dichotomous , that is , yes - or - no - type rather than more - or - less ...
... Uncertainty Most of our traditional tools for formal modeling , reasoning , and computing are crisp , deterministic , and precise in character . By crisp we mean dichotomous , that is , yes - or - no - type rather than more - or - less ...
Page 3
... uncertainty ( stochastic character ) has long been handled appropriately by probability theory and statistics . This Kolmogoroff - type probability is essentially frequentistic and is based on set - theoretic considerations . Koopman's ...
... uncertainty ( stochastic character ) has long been handled appropriately by probability theory and statistics . This Kolmogoroff - type probability is essentially frequentistic and is based on set - theoretic considerations . Koopman's ...
Page 6
... uncertainties . In general , however , they do not even define sufficiently or only in a very specific and limited sense what is meant by “ uncertainty ” . I believe that uncertainty , if considered as a subjective phenomenon , can and ...
... uncertainties . In general , however , they do not even define sufficiently or only in a very specific and limited sense what is meant by “ uncertainty ” . I believe that uncertainty , if considered as a subjective phenomenon , can and ...
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