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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Page xi
... values for variable “significance". Linguistic evaluation values of lathes B, C, D, E. 285 285 286 287 287 288 295 295 300 303 304 304 305 307 309 309 Figure 15–5 Figure 15–6 Figure 15–7 Figure 15–8 Figure 15–9 LIST OF FIGURES xi.
... values for variable “significance". Linguistic evaluation values of lathes B, C, D, E. 285 285 286 287 287 288 295 295 300 303 304 304 305 307 309 309 Figure 15–5 Figure 15–6 Figure 15–7 Figure 15–8 Figure 15–9 LIST OF FIGURES xi.
Page 1
Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known, and that there are no doubts about their values or their occurrence. If the model under consideration is a formal model ...
Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known, and that there are no doubts about their values or their occurrence. If the model under consideration is a formal model ...
Page 7
One of the reasons for this might be, that expert systems in their inference engines, when they are based on dual logic, perform symbol processing (truth values true or false) rather than knowledge processing.
One of the reasons for this might be, that expert systems in their inference engines, when they are based on dual logic, perform symbol processing (truth values true or false) rather than knowledge processing.
Page 13
It has already been mentioned that the membership function is not limited to values between 0 and 1. If suppla(x) = 1, the fuzzy set A is called normal. A nonempty fuzzy set A can always be normalized by dividing pi(x) by suppli(x).
It has already been mentioned that the membership function is not limited to values between 0 and 1. If suppla(x) = 1, the fuzzy set A is called normal. A nonempty fuzzy set A can always be normalized by dividing pi(x) by suppli(x).
Page 18
We shall therefore sketch their reasoning: Consider two statements, S and T, for which the truth values are pus and pur, respectively, ps, pure [0, 1]. The truth. 18 FUZZY SET THEORY-AND ITS APPLICATIONS.
We shall therefore sketch their reasoning: Consider two statements, S and T, for which the truth values are pus and pur, respectively, ps, pure [0, 1]. The truth. 18 FUZZY SET THEORY-AND ITS APPLICATIONS.
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Contents
| 9 | |
| 11 | |
| 16 | |
| 22 | |
| 29 | |
Criteria for Selecting Appropriate Aggregation Operators | 43 |
The Extension Principle and Applications | 54 |
Special Extended Operations | 61 |
Applicationoriented Modeling of Uncertainty | 111 |
Linguistic Variables | 140 |
Fuzzy Data Bases and Queries | 265 |
Decision Making in Fuzzy Environments | 329 |
Applications of Fuzzy Sets in Engineering and Management | 371 |
Empirical Research in Fuzzy Set Theory | 443 |
Future Perspectives | 477 |
181 | 485 |
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Common terms and phrases
aggregation algorithm analysis applications approach appropriate approximately areas assignment assume base called chapter classical clustering compute concepts considered constraints contains corresponding crisp criteria customers decision defined definition degree of membership depends described determine discussed distribution domain elements engineering example exist expert systems expressed extension Figure fuzzy control fuzzy numbers fuzzy set theory given goal human important indicate inference input instance integral interpreted intersection interval knowledge linguistic variable logic mathematical mean measure membership function methods normally objective objective function observed obtain operators optimal positive possible probability problem programming properties provides reasoning relation representing require respect rules scale shown shows similarity situation solution space specific statement structure suggested t-norms Table tion true truth uncertainty values Zadeh
Bibliographic information
| Title | Fuzzy Set Theory—and Its Applications SpringerLink : Bücher |
| Author | Hans-Jürgen Zimmermann |
| Edition | 4, illustrated |
| Publisher | Springer Science & Business Media, 2011 |
| ISBN | 9401006466, 9789401006460 |
| Length | 514 pages |
| Subjects | › › Business & Economics / Operations Research Computers / Artificial Intelligence / General Mathematics / General Mathematics / History & Philosophy Mathematics / Logic |
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