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
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Page v
... Fuzzy Sets Algebraic Operations Set-Theoretic Operations Criteria for Selecting Appropriate Aggregation Operators Fuzzy Measures and Measures of Fuzziness Fuzzy Measures Measures of Fuzziness The Extension Principle and Applications ...
... Fuzzy Sets Algebraic Operations Set-Theoretic Operations Criteria for Selecting Appropriate Aggregation Operators Fuzzy Measures and Measures of Fuzziness Fuzzy Measures Measures of Fuzziness The Extension Principle and Applications ...
Page vi
... Possibility Theory Fuzzy Sets and Possibility Distributions Possibility and Necessity Measures Probability of Fuzzy Events Probability of a Fuzzy Event as a Scalar Probability of a Fuzzy Event as a Fuzzy Set Possibility vs.
... Possibility Theory Fuzzy Sets and Possibility Distributions Possibility and Necessity Measures Probability of Fuzzy Events Probability of a Fuzzy Event as a Scalar Probability of a Fuzzy Event as a Fuzzy Set Possibility vs.
Page 6
It will mean different things, depending on the application area and the way it is measured. In the meantime, numerous authors have contributed to this theory. In 1984, as many as 4,000 publications have already existed and in 2000 ...
It will mean different things, depending on the application area and the way it is measured. In the meantime, numerous authors have contributed to this theory. In 1984, as many as 4,000 publications have already existed and in 2000 ...
Page 9
Chapter 4 is devoted to fuzzy measures, measures of fuzziness, and other important measures that are needed for applications presented either in Part II of this book or in the second volume on decision making in a fuzzy environment.
Chapter 4 is devoted to fuzzy measures, measures of fuzziness, and other important measures that are needed for applications presented either in Part II of this book or in the second volume on decision making in a fuzzy environment.
Page 24
From a practical point of view, such type m fuzzy sets for large m (even for m 2 3) are hard to deal with, and it will be extremely difficult or even impossible to measure them or to visualize them. We will, therefore, not even try to ...
From a practical point of view, such type m fuzzy sets for large m (even for m 2 3) are hard to deal with, and it will be extremely difficult or even impossible to measure them or to visualize them. We will, therefore, not even try to ...
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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 |
| Export Citation | BiBTeX EndNote RefMan |