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 81
Page 3
... crisp and deterministic , and they cannot be described precisely . 2. The complete description of a real system often would require far more detailed data than a human being could ever recognize simultaneously , process , and understand ...
... crisp and deterministic , and they cannot be described precisely . 2. The complete description of a real system often would require far more detailed data than a human being could ever recognize simultaneously , process , and understand ...
Page 11
... ( crisp ) set is normally defined as a collection of elements or objects x = X that can be finite , countable , or overcountable . Each single element can either belong to or not belong to a set A , A≤ X. In the former case , the ...
... ( crisp ) set is normally defined as a collection of elements or objects x = X that can be finite , countable , or overcountable . Each single element can either belong to or not belong to a set A , A≤ X. In the former case , the ...
Page 13
... ( crisp ) set X , some elements of a fuzzy set may have the degree of membership zero . Often it is appropriate to consider those elements of the universe that have a nonzero degree of membership in a fuzzy set . Definition 2-2 The ...
... ( crisp ) set X , some elements of a fuzzy set may have the degree of membership zero . Often it is appropriate to consider those elements of the universe that have a nonzero degree of membership in a fuzzy set . Definition 2-2 The ...
Page 14
... crisp set of all xe X such that μA ( x ) > 0 . Example 2-2 Let us consider example 2-1a again : The support of S ( Ã ) = { 1 , 2 , 3 , 4 , 5 , 6 } . The elements ( types of houses ) { 7 , 8 , 9 , 10 } are not part of the support of A ...
... crisp set of all xe X such that μA ( x ) > 0 . Example 2-2 Let us consider example 2-1a again : The support of S ( Ã ) = { 1 , 2 , 3 , 4 , 5 , 6 } . The elements ( types of houses ) { 7 , 8 , 9 , 10 } are not part of the support of A ...
Page 22
... crisp functions , and the operations corresponded essentially to the operations of dual logic or Boolean algebra . Different extensions of the basic concept discussed in chapter 2 are possible . They may concern the definition of a ...
... crisp functions , and the operations corresponded essentially to the operations of dual logic or Boolean algebra . Different extensions of the basic concept discussed in chapter 2 are possible . They may concern the definition of a ...
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 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