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 53
Page xii
The membership function of the fuzzy goal G. The solution of the numerical example. Structure of OPAL. Fuzzy sets for the ratio in the “if” part of the rules. Example of an FMS [Hartley 1984, p. 194]. Criteria hierarchies.
The membership function of the fuzzy goal G. The solution of the numerical example. Structure of OPAL. Fuzzy sets for the ratio in the “if” part of the rules. Example of an FMS [Hartley 1984, p. 194]. Criteria hierarchies.
Page xiv
Solution to transportation problem. Membership grades for slack time and waiting time. Membership grades for conditional parts of the rules. Membership grades for the rules. Results. Definition of linguistic variables [Rinks 1982].
Solution to transportation problem. Membership grades for slack time and waiting time. Membership grades for conditional parts of the rules. Membership grades for the rules. Results. Definition of linguistic variables [Rinks 1982].
Page xv
He shows through a wealth of examples the ways in which the theory can be applied to the solution of realistic problems, particularly in the realm of decision analysis, and motivates the theory by applications in which fuzzy sets play ...
He shows through a wealth of examples the ways in which the theory can be applied to the solution of realistic problems, particularly in the realm of decision analysis, and motivates the theory by applications in which fuzzy sets play ...
Page 1
In set theory, an element can either belong to a set or not; and in optimization, a solution is either feasible or not. Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modeled ...
In set theory, an element can either belong to a set or not; and in optimization, a solution is either feasible or not. Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modeled ...
Page 7
... and arrive at membership functions of fuzzy sets, which can then be retranslated into words and sentences via linguistic approximation. e) Efficient Determination of Approximate Solutions Already in the 70s INTRODUCTION TO FUZZY SETS 7.
... and arrive at membership functions of fuzzy sets, which can then be retranslated into words and sentences via linguistic approximation. e) Efficient Determination of Approximate Solutions Already in the 70s INTRODUCTION TO FUZZY SETS 7.
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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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