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 ix
Triangular fuzzy numbers representing a fuzzy function. The maximum of a fuzzy function. Fuzzily bounded interval. Uncertainty as situational property. Probability of a fuzzy event. Linguistic variable “Age".
Triangular fuzzy numbers representing a fuzzy function. The maximum of a fuzzy function. Fuzzily bounded interval. Uncertainty as situational property. Probability of a fuzzy event. Linguistic variable “Age".
Page xi
Fuzzy sets representing weights and ratings. Final ratings of alternatives. Preferability of alternative 2 over all others. Linguistic values for variable “rigidity". Linguistic values for variable “elements' rigidity".
Fuzzy sets representing weights and ratings. Final ratings of alternatives. Preferability of alternative 2 over all others. Linguistic values for variable “rigidity". Linguistic values for variable “elements' rigidity".
Page 12
A fuzzy set is represented solely by stating its membership function [for instance, Negoita and Ralescu 1975]. uR(x) 1 5 1 O 1 5 × Figure 2–1. 12 FUZZY SET THEORY-AND ITS APPLICATIONS.
A fuzzy set is represented solely by stating its membership function [for instance, Negoita and Ralescu 1975]. uR(x) 1 5 1 O 1 5 × Figure 2–1. 12 FUZZY SET THEORY-AND ITS APPLICATIONS.
Page 25
Further attempts at representing vague and uncertain data with different types of fuzzy sets were made by Atanassov and Stoeva [Atanassov and Stoeva 1983; Atanassov 1986], who defined a generalization of the notion of fuzzy sets— the ...
Further attempts at representing vague and uncertain data with different types of fuzzy sets were made by Atanassov and Stoeva [Atanassov and Stoeva 1983; Atanassov 1986], who defined a generalization of the notion of fuzzy sets— the ...
Page 27
... U representing a concept of interest, the approximation space A = (U, R) can be characterized by three distinct regions of X in A: the socalled positive region A(X), the boundary region A(X) – A(X), and the negative region U – A(X).
... U representing a concept of interest, the approximation space A = (U, R) can be characterized by three distinct regions of X in A: the socalled positive region A(X), the boundary region A(X) – A(X), and the negative region U – A(X).
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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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