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 6
... conceptual phenomena can be precisely and rigorously studied . It can also be considered as a modeling language well ... concepts as well as by " embrac- ing " classical mathematical areas such as algebra , graph theory , topology , and ...
... conceptual phenomena can be precisely and rigorously studied . It can also be considered as a modeling language well ... concepts as well as by " embrac- ing " classical mathematical areas such as algebra , graph theory , topology , and ...
Page 9
... concepts and alternative operators . Chapter 4 is devoted to fuzzy measures , measures of fuzziness , and other important measures that are needed for applications presented either in Part II of this book or in the second volume on ...
... concepts and alternative operators . Chapter 4 is devoted to fuzzy measures , measures of fuzziness , and other important measures that are needed for applications presented either in Part II of this book or in the second volume on ...
Page 16
... concepts suggested by Zadeh in 1965 [ Zadeh 1965 , p . 310 ] . They constitute a consistent framework for the theory of fuzzy sets . They are , however , not the only possible way to extend classical set theory consistently . Zadeh and ...
... concepts suggested by Zadeh in 1965 [ Zadeh 1965 , p . 310 ] . They constitute a consistent framework for the theory of fuzzy sets . They are , however , not the only possible way to extend classical set theory consistently . Zadeh and ...
Page 22
... concept discussed in chapter 2 are possible . They may concern the definition of a fuzzy set or they may concern the opera- tions with fuzzy sets . With respect to the definition of ... concepts will be Extensions 23 1 Types of Fuzzy Sets 23.
... concept discussed in chapter 2 are possible . They may concern the definition of a fuzzy set or they may concern the opera- tions with fuzzy sets . With respect to the definition of ... concepts will be Extensions 23 1 Types of Fuzzy Sets 23.
Page 24
Hans-Jürgen Zimmermann. mathematical models can be conceived . These concepts will be discussed in section 3.2 . So far we have considered fuzzy sets with crisply defined membership func- tions or degrees of membership . It is doubtful ...
Hans-Jürgen Zimmermann. mathematical models can be conceived . These concepts will be discussed in section 3.2 . So far we have considered fuzzy sets with crisply defined membership func- tions or degrees of membership . It is doubtful ...
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