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 1-5 of 52
Page v
... Appropriate Aggregation Operators 43 4 Fuzzy Measures and Measures of Fuzziness 47 4.1 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 ...
... Appropriate Aggregation Operators 43 4 Fuzzy Measures and Measures of Fuzziness 47 4.1 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 ...
Page xvii
... appropriate and necessary . On the other hand , theoretical publications are already so specialized and assume such a back- ground in fuzzy set theory that they are hard to understand . The more than 4,000 publications that exist in the ...
... appropriate and necessary . On the other hand , theoretical publications are already so specialized and assume such a back- ground in fuzzy set theory that they are hard to understand . The more than 4,000 publications that exist in the ...
Page 2
... appropriately . The utter importance of the modeling language is recognized by Apostel , when he says : The relationship between formal languages and domains in which they have models must in the empirical sciences necessarily be guided ...
... appropriately . The utter importance of the modeling language is recognized by Apostel , when he says : The relationship between formal languages and domains in which they have models must in the empirical sciences necessarily be guided ...
Page 3
... appropriately by probability theory and statistics . This Kolmogoroff - type probability is essentially frequentistic and is based on set - theoretic considerations . Koopman's probability refers to the truth of statements and therefore ...
... appropriately by probability theory and statistics . This Kolmogoroff - type probability is essentially frequentistic and is based on set - theoretic considerations . Koopman's probability refers to the truth of statements and therefore ...
Page 8
... appropriate detail . The present book will there- fore proceed as follows : Part I of this book , containing chapters 2 to 8 , will develop the formal frame- work of fuzzy mathematics . Due to space limitations and for didactical ...
... appropriate detail . The present book will there- fore proceed as follows : Part I of this book , containing chapters 2 to 8 , will develop the formal frame- work of fuzzy mathematics . Due to space limitations and for didactical ...
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