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
Results 6-10 of 54
Page 22
... space was assumed to be the space of real numbers , membership functions were crisp functions , and the operations corresponded essentially to the operations of dual logic or Boolean algebra . Different extensions of the basic concept ...
... space was assumed to be the space of real numbers , membership functions were crisp functions , and the operations corresponded essentially to the operations of dual logic or Boolean algebra . Different extensions of the basic concept ...
Page 25
... space . One of the main advantages of the notion of probabilistic sets in modeling fuzzy and stochastic features of a system is asserted to be the applicability of moment analysis , that is , the possibility of computing moments such as ...
... space . One of the main advantages of the notion of probabilistic sets in modeling fuzzy and stochastic features of a system is asserted to be the applicability of moment analysis , that is , the possibility of computing moments such as ...
Page 27
... space of X in A , then “ x surely belongs to X in A , ” x e Ć ( X ) means that " x possibly belongs to X in A. ” For the subset X U representing a concept of interest , the approximation space A = ( U , R ) can be characterized by three ...
... space of X in A , then “ x surely belongs to X in A , ” x e Ć ( X ) means that " x possibly belongs to X in A. ” For the subset X U representing a concept of interest , the approximation space A = ( U , R ) can be characterized by three ...
Page 28
... space XX ... XX , with the membership function Definition 3-7 μ ( Ć1x ... xĆn ) ( x ) = min { μĆ ; ( x ; ) | x = ( x1 , ...... . Xn ) , X” ¤ X ; } i The mth power of a fuzzy set Ć is a fuzzy set with the membership function μ1m ( x ) ...
... space XX ... XX , with the membership function Definition 3-7 μ ( Ć1x ... xĆn ) ( x ) = min { μĆ ; ( x ; ) | x = ( x1 , ...... . Xn ) , X” ¤ X ; } i The mth power of a fuzzy set Ć is a fuzzy set with the membership function μ1m ( x ) ...
Page 30
... spaces where probability distributions rather than numbers are used in order to describe the distance between two elements in the respective space . Berthold Schweizer and Abe Sklar [ Schweizer and Sklar 1961 ] provided the axioms of t ...
... spaces where probability distributions rather than numbers are used in order to describe the distance between two elements in the respective space . Berthold Schweizer and Abe Sklar [ Schweizer and Sklar 1961 ] provided the axioms of t ...
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 |
Other editions - View all
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