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 xvi
... thanked for contributing so much over the past decade to the advancement of the theory of fuzzy sets as a scientist, educator, administrator, and organizer. L.A. Zadeh Since its inception 20 years ago, the theory of fuzzy xvi FOREWORD.
... thanked for contributing so much over the past decade to the advancement of the theory of fuzzy sets as a scientist, educator, administrator, and organizer. L.A. Zadeh Since its inception 20 years ago, the theory of fuzzy xvi FOREWORD.
Page 3
L. Zadeh referred to the second point when he wrote, “As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision ...
L. Zadeh referred to the second point when he wrote, “As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision ...
Page 5
1.2 Fuzzy Set Theory The first publications in fuzzy set theory by Zadeh [1965) and Goguen [1967, 1969] show the intention of the authors to generalize the classical notion of a set and a proposition [statement] to accommodate fuzziness ...
1.2 Fuzzy Set Theory The first publications in fuzzy set theory by Zadeh [1965) and Goguen [1967, 1969] show the intention of the authors to generalize the classical notion of a set and a proposition [statement] to accommodate fuzziness ...
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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 15
One final feature of a fuzzy set, which we will use frequently in later chapters, is its cardinality or “power” [Zadeh 1981c]. Definition 2–5 For a finite fuzzy set A, the cardinality. FUZZY SETS-BASIC DEFINITIONS 15.
One final feature of a fuzzy set, which we will use frequently in later chapters, is its cardinality or “power” [Zadeh 1981c]. Definition 2–5 For a finite fuzzy set A, the cardinality. FUZZY SETS-BASIC DEFINITIONS 15.
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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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