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 v
... Extensions 23 3.1 Types of Fuzzy Sets 23 3.2 Further Operations on Fuzzy Sets 27 3.2.1 Algebraic Operations 28 3.2.2 ... Extension Principle 55 5.2 Operations for Type 2 Fuzzy Sets 56 5.3 Algebraic Operations with Fuzzy Numbers 59 5.3.1 ...
... Extensions 23 3.1 Types of Fuzzy Sets 23 3.2 Further Operations on Fuzzy Sets 27 3.2.1 Algebraic Operations 28 3.2.2 ... Extension Principle 55 5.2 Operations for Type 2 Fuzzy Sets 56 5.3 Algebraic Operations with Fuzzy Numbers 59 5.3.1 ...
Page vii
... Extensions 262 12 Fuzzy Data Bases and Queries 265 12.1 Introduction 265 12.2 Fuzzy Relational Databases 266 12.3 Fuzzy Queries in Crisp Databases 268 13 Fuzzy Data Analysis 277 13.1 Introduction 277 13.2 Methods for Fuzzy Data Analysis ...
... Extensions 262 12 Fuzzy Data Bases and Queries 265 12.1 Introduction 265 12.2 Fuzzy Relational Databases 266 12.3 Fuzzy Queries in Crisp Databases 268 13 Fuzzy Data Analysis 277 13.1 Introduction 277 13.2 Methods for Fuzzy Data Analysis ...
Page ix
... extension principle . Figure 5-2 Trapezoidal " fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 Figure 6-2 Fuzzy forests . 86 Figure 6-3 Graphs that are not forests ...
... extension principle . Figure 5-2 Trapezoidal " fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 Figure 6-2 Fuzzy forests . 86 Figure 6-3 Graphs that are not forests ...
Page xviii
... extensions in enough detail to be comprehended by those who have not been exposed to fuzzy set theory . Examples and exercises serve to illustrate the concepts even more clearly . For the interested or more advanced reader , numerous ...
... extensions in enough detail to be comprehended by those who have not been exposed to fuzzy set theory . Examples and exercises serve to illustrate the concepts even more clearly . For the interested or more advanced reader , numerous ...
Page xxiv
... extension of the chapter on data mining and a new chapter on fuzzy sets in data bases . The following figure indicates the development of fuzzy set theory from another point of view : Academic Stage Consolidation and Integration Theory ...
... extension of the chapter on data mining and a new chapter on fuzzy sets in data bases . The following figure indicates the development of fuzzy set theory from another point of view : Academic Stage Consolidation and Integration Theory ...
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