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 xxiv
... indicates the development of fuzzy set theory from another point of view : Academic Stage Consolidation and Integration Theory Survey of Evolution Fuzzy Sets Fuzzy Decision Fuzzy Linear Programing Fuzzy Control Linguistie Varables Fuzzy ...
... indicates the development of fuzzy set theory from another point of view : Academic Stage Consolidation and Integration Theory Survey of Evolution Fuzzy Sets Fuzzy Decision Fuzzy Linear Programing Fuzzy Control Linguistie Varables Fuzzy ...
Page 1
... indicates that we assume the structures and parameters of the model to be definitely known , and that there are no doubts about their values or their occurrence . If the model under consideration is a formal model [ Zimmermann 1980 , p ...
... indicates that we assume the structures and parameters of the model to be definitely known , and that there are no doubts about their values or their occurrence . If the model under consideration is a formal model [ Zimmermann 1980 , p ...
Page 8
... indicated or described . The character of these chap- ters will obviously have to be formal . Part II of the book , chapters 9 to 16 , will then survey the most interesting applications of fuzzy set theory . At that stage the student ...
... indicated or described . The character of these chap- ters will obviously have to be formal . Part II of the book , chapters 9 to 16 , will then survey the most interesting applications of fuzzy set theory . At that stage the student ...
Page 11
... indicates mem- bership and 0 nonmembership . For a fuzzy set , the characteristic function allows . various degrees of membership for the elements of a given set . Definition 2-1 If X is a collection of objects denoted generically by x ...
... indicates mem- bership and 0 nonmembership . For a fuzzy set , the characteristic function allows . various degrees of membership for the elements of a given set . Definition 2-1 If X is a collection of objects denoted generically by x ...
Page 25
... indicates the difference between the appearance of fuzzy sets and probabilistic sets [ Hirota 1981 , p . 33 ] . Of course , the mathematical pro- perties of probabilistic sets differ from those of fuzzy sets , and so do the math ...
... indicates the difference between the appearance of fuzzy sets and probabilistic sets [ Hirota 1981 , p . 33 ] . Of course , the mathematical pro- perties of probabilistic sets differ from those of fuzzy sets , and so do the math ...
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