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. |
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Results 6-10 of 46
Page 19
... intersection ) and v for " or " ( = union ) , these assump- tions amount to the following seven restrictions , to be imposed on the two com- mutative ( see ( ii ) ) and associative ( see ( vi ) ) binary compositions and on the closed ...
... intersection ) and v for " or " ( = union ) , these assump- tions amount to the following seven restrictions , to be imposed on the two com- mutative ( see ( ii ) ) and associative ( see ( vi ) ) binary compositions and on the closed ...
Page 20
... intersection and union ) should also be continuous and monotonically decreasing , and we would like the complement of the complement to be the original statement ( in order to be in line with traditional logic and set theory ) . These ...
... intersection and union ) should also be continuous and monotonically decreasing , and we would like the complement of the complement to be the original statement ( in order to be in line with traditional logic and set theory ) . These ...
Page 21
... intersections and unions of the following fuzzy sets : a . The fuzzy sets A , B , and C from exercise 4 b . B and C from exercise 2 6. Determine the intersection and the union of the complements of fuzzy sets B and C from exercise 4 . 3 ...
... intersections and unions of the following fuzzy sets : a . The fuzzy sets A , B , and C from exercise 4 b . B and C from exercise 2 6. Determine the intersection and the union of the complements of fuzzy sets B and C from exercise 4 . 3 ...
Page 22
... intersection , which in turn is modeled by the min - operator . The same type of relationship was assumed for the logical " or , " the union , and the max - operator . Departing from the well - established systems of dual logic and ...
... intersection , which in turn is modeled by the min - operator . The same type of relationship was assumed for the logical " or , " the union , and the max - operator . Departing from the well - established systems of dual logic and ...
Page 24
... intersection , union , and complement defined so far are no longer adequate for type 2 fuzzy sets . We will , however , postpone the discussions for adequate operators until section 5.2 , that is , until we have presented the exten ...
... intersection , union , and complement defined so far are no longer adequate for type 2 fuzzy sets . We will , however , postpone the discussions for adequate operators until section 5.2 , that is , until we have presented the exten ...
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