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 v
... Fuzzy Measures 47 4.2 Measures of Fuzziness 49 5 The Extension Principle and Applications 55 5.1 The Extension Principle 55 5.2 Operations for Type 2 Fuzzy Sets 56 5.3 Algebraic Operations with Fuzzy Numbers 59 5.3.1 Special Extended ...
... Fuzzy Measures 47 4.2 Measures of Fuzziness 49 5 The Extension Principle and Applications 55 5.1 The Extension Principle 55 5.2 Operations for Type 2 Fuzzy Sets 56 5.3 Algebraic Operations with Fuzzy Numbers 59 5.3.1 Special Extended ...
Page ix
... fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 Figure 6-2 Fuzzy forests . 86 Figure 6-3 Graphs that are not forests . 86 Figure 7-1 Maximizing set . 96 Figure 7-2 A ...
... fuzzy number " . Figure 5-3 LR - representation of fuzzy numbers . 88 788 26 38 57 60 65 Figure 6-1 Fuzzy graphs . 84 Figure 6-2 Fuzzy forests . 86 Figure 6-3 Graphs that are not forests . 86 Figure 7-1 Maximizing set . 96 Figure 7-2 A ...
Page 12
... numbers whose supremum is finite . Elements with a zero degree of membership are normally not listed . Example 2 - la A realtor wants to classify the house he offers to his clients . One ... numbers 12 FUZZY SET THEORY - AND ITS APPLICATIONS.
... numbers whose supremum is finite . Elements with a zero degree of membership are normally not listed . Example 2 - la A realtor wants to classify the house he offers to his clients . One ... numbers 12 FUZZY SET THEORY - AND ITS APPLICATIONS.
Page 13
... numbers close to 10 " A à = √R 1 1+ ( x - 10 ) 2 X It has already been mentioned that the membership function is not limited to values between 0 and 1. If sup ̧μà ( x ) = 1 , the fuzzy set à is called normal . A non- empty fuzzy set A ...
... numbers close to 10 " A à = √R 1 1+ ( x - 10 ) 2 X It has already been mentioned that the membership function is not limited to values between 0 and 1. If sup ̧μà ( x ) = 1 , the fuzzy set à is called normal . A non- empty fuzzy set A ...
Page 20
... fuzzy sets : a . Large integers b . Very small numbers c . Medium - sized men d . Numbers approximately between 10 and 20 e . High speeds for racing cars 2. Determine all a - level sets and all strong a - level sets for the following fuzzy ...
... fuzzy sets : a . Large integers b . Very small numbers c . Medium - sized men d . Numbers approximately between 10 and 20 e . High speeds for racing cars 2. Determine all a - level sets and all strong a - level sets for the following fuzzy ...
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