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 2
... they are in a sense produced through and for each other; (b) extensions of formalisms and models must necessarily be considered because everything introduced is introduced to make progress in the description of the objects studied.
... they are in a sense produced through and for each other; (b) extensions of formalisms and models must necessarily be considered because everything introduced is introduced to make progress in the description of the objects studied.
Page 6
It can also be considered as a modeling language well suited for situations in which fuzzy relations, criteria, and phenomena exist. Fuzziness has so far not been defined uniquely semantically, and probably never will be.
It can also be considered as a modeling language well suited for situations in which fuzzy relations, criteria, and phenomena exist. Fuzziness has so far not been defined uniquely semantically, and probably never will be.
Page 8
Zadeh expressed his intention to have fuzzy set theory considered as a tool to determine approximate solutions of real problems in an efficient or affordable way. This goal has never really been achieved successfully.
Zadeh expressed his intention to have fuzzy set theory considered as a tool to determine approximate solutions of real problems in an efficient or affordable way. This goal has never really been achieved successfully.
Page 24
So far we have considered fuzzy sets with crisply defined membership functions or degrees of membership. It is doubtful whether, for instance, human beings have or can have a crisp image of membership functions in their minds.
So far we have considered fuzzy sets with crisply defined membership functions or degrees of membership. It is doubtful whether, for instance, human beings have or can have a crisp image of membership functions in their minds.
Page 31
The max-operator, algebraic sum, and bounded sum considered above belong to this class. Definition 3–13 [Dubois and Prade 1985, p. 90) t-conorms or s-norms are associative, commutative, and monotonic two-placed functions s that map from ...
The max-operator, algebraic sum, and bounded sum considered above belong to this class. Definition 3–13 [Dubois and Prade 1985, p. 90) t-conorms or s-norms are associative, commutative, and monotonic two-placed functions s that map from ...
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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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