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 vi
... Methods 118 8.1.4 Uncertainty Theories as Transformers of Information 119 8.1.5 Matching Uncertainty Theory and Uncertain Phenomena 120 8.2 Possibility Theory 122 8.2.1 Fuzzy Sets and Possibility Distributions 122 8.2.2 Possibility and ...
... Methods 118 8.1.4 Uncertainty Theories as Transformers of Information 119 8.1.5 Matching Uncertainty Theory and Uncertain Phenomena 120 8.2 Possibility Theory 122 8.2.1 Fuzzy Sets and Possibility Distributions 122 8.2.2 Possibility and ...
Page vii
... Methods for Fuzzy Data Analysis 279 13.2.1 Algorithmic Approaches 281 13.2.2 Knowledge - Based Approaches 302 13.2.3 Neural Net Approaches 304 13.3 Dynamic Fuzzy Data Analysis 306 13.3.1 Problem Description 306 13.3.2 Similarity of ...
... Methods for Fuzzy Data Analysis 279 13.2.1 Algorithmic Approaches 281 13.2.2 Knowledge - Based Approaches 302 13.2.3 Neural Net Approaches 304 13.3 Dynamic Fuzzy Data Analysis 306 13.3.1 Problem Description 306 13.3.2 Similarity of ...
Page xv
... methods based on probability theory and bivalent logic . Nevertheless , a question that is frequently raised by the skeptics is : Are there , in fact , any significant problem - areas in which the use of the theory of fuzzy sets leads ...
... methods based on probability theory and bivalent logic . Nevertheless , a question that is frequently raised by the skeptics is : Are there , in fact , any significant problem - areas in which the use of the theory of fuzzy sets leads ...
Page xxiii
... methods , that combine the strengths of both of these areas . Nevertheless , all three areas are continuing to develop new approaches in their own areas . For a textbook it would be inadequate to cover the basics of fuzzy set theory and ...
... methods , that combine the strengths of both of these areas . Nevertheless , all three areas are continuing to develop new approaches in their own areas . For a textbook it would be inadequate to cover the basics of fuzzy set theory and ...
Page 6
... methods in many cases and as an attractive “ add - on ” to classical approaches in other cases . In this context it may be useful to cite and comment the major goals of this tech- nology briefly and to correct the still very common view ...
... methods in many cases and as an attractive “ add - on ” to classical approaches in other cases . In this context it may be useful to cite and comment the major goals of this tech- nology briefly and to correct the still very common view ...
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