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 xvii
On the other hand, theoretical publications are already so specialized and assume such a background in fuzzy set theory that they are hard to understand. The more than 4,000 publications that exist in the field are widely scattered over ...
On the other hand, theoretical publications are already so specialized and assume such a background in fuzzy set theory that they are hard to understand. The more than 4,000 publications that exist in the field are widely scattered over ...
Page xviii
Even though no specific mathematical background is necessary to understand the books, it is assumed that the students have some background in calculus, set theory, operations research, and decision theory. I would like to acknowledge ...
Even though no specific mathematical background is necessary to understand the books, it is assumed that the students have some background in calculus, set theory, operations research, and decision theory. I would like to acknowledge ...
Page 1
Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modeled or ... Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known, ...
Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modeled or ... Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known, ...
Page 3
In 1923 the philosopher B. Russell [1923] referred to the first point when he wrote: All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life but only to ...
In 1923 the philosopher B. Russell [1923] referred to the first point when he wrote: All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life but only to ...
Page 13
As a matter of convenience, we will generally assume that fuzzy sets are normalized. For the representation of fuzzy sets, we will use the notation 1 illustrated in examples 2–1b and 2–1c, respectively. A fuzzy set is obviously a ...
As a matter of convenience, we will generally assume that fuzzy sets are normalized. For the representation of fuzzy sets, we will use the notation 1 illustrated in examples 2–1b and 2–1c, respectively. A fuzzy set is obviously a ...
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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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