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 v
... Uncertainty Fuzzy Set Theory ix xiii XV xvii xix 112 2 Part I : Fuzzy Mathematics 9 22 Fuzzy Sets - Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set - Theoretic Operations for Fuzzy Sets 16 3 Extensions 23 3.1 Types of Fuzzy ...
... Uncertainty Fuzzy Set Theory ix xiii XV xvii xix 112 2 Part I : Fuzzy Mathematics 9 22 Fuzzy Sets - Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set - Theoretic Operations for Fuzzy Sets 16 3 Extensions 23 3.1 Types of Fuzzy ...
Page vi
... Uncertainty Modeling 111 8.1 Application - oriented Modeling of Uncertainty 111 8.1.1 Causes of Uncertainty 114 8.1.2 Type of Available Information 117 8.1.3 Uncertainty Methods 118 8.1.4 Uncertainty Theories as Transformers of ...
... Uncertainty Modeling 111 8.1 Application - oriented Modeling of Uncertainty 111 8.1.1 Causes of Uncertainty 114 8.1.2 Type of Available Information 117 8.1.3 Uncertainty Methods 118 8.1.4 Uncertainty Theories as Transformers of ...
Page vii
... Uncertainty Modeling in Expert Systems 193 10.3 Applications 203 11 Fuzzy Control 223 11.1 Origin and Objective 223 11.2 Automatic Control 225 11.3 The Fuzzy Controller 226 11.4 Types of Fuzzy Controllers 228 11.4.1 The Mamdani ...
... Uncertainty Modeling in Expert Systems 193 10.3 Applications 203 11 Fuzzy Control 223 11.1 Origin and Objective 223 11.2 Automatic Control 225 11.3 The Fuzzy Controller 226 11.4 Types of Fuzzy Controllers 228 11.4.1 The Mamdani ...
Page xiii
... uncertainty properties . 121 Table 8-2 Possibility functions . 128 Table 8-3 Koopman's vs. Kolmogoroff's probabilities . 136 Table 8-4 Relationship between Boolean algebra , probabilities , and possibilities . 137 Table 9-1 Formal ...
... uncertainty properties . 121 Table 8-2 Possibility functions . 128 Table 8-3 Koopman's vs. Kolmogoroff's probabilities . 136 Table 8-4 Relationship between Boolean algebra , probabilities , and possibilities . 137 Table 9-1 Formal ...
Page xvi
... uncertainty in expert systems , and in appli- cations of the theory of fuzzy sets to decision analysis . As one of the leading contributors to and practitioners of the use of fuzzy sets in decision analysis , Professor Zimmermann is ...
... uncertainty in expert systems , and in appli- cations of the theory of fuzzy sets to decision analysis . As one of the leading contributors to and practitioners of the use of fuzzy sets in decision analysis , Professor Zimmermann is ...
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