Open AccessBook
Fuzzy sets and systems
Lotfi A. Zadeh
- pp 35-43
TLDR
Fuzzy sets as mentioned in this paper are a class of classes in which there may be grades of membership intermediate between full membership and non-membership, i.e., a fuzzy set is characterized by a membership function which assigns to each object its grade of membership.Abstract:
The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...read more
Citations
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An Introduction to Fuzzy Control
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Linguistic decision analysis: steps for solving decision problems under linguistic information
TL;DR: A study on the steps to follow in linguistic decision analysis is presented in a context of multi-criteria/multi-person decision making.
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The logic of inexact concepts
TL;DR: This paper examines problems of vagueness, ambiguity, and ambivalence by suggesting a method for constructing and studying models of the way the authors use words, called a 'logic of inexact concepts'.
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Ten years of genetic fuzzy systems: current framework and new trends
TL;DR: The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems.
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Entropy for intuitionistic fuzzy sets
Eulalia Szmidt,Janusz Kacprzyk +1 more
TL;DR: It is shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .
References
More filters
Book
An Introduction to Fuzzy Control
TL;DR: Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic that can be found either as stand-alone control elements or as int ...
Journal ArticleDOI
Linguistic decision analysis: steps for solving decision problems under linguistic information
TL;DR: A study on the steps to follow in linguistic decision analysis is presented in a context of multi-criteria/multi-person decision making.
Journal ArticleDOI
The logic of inexact concepts
TL;DR: This paper examines problems of vagueness, ambiguity, and ambivalence by suggesting a method for constructing and studying models of the way the authors use words, called a 'logic of inexact concepts'.
Journal ArticleDOI
Ten years of genetic fuzzy systems: current framework and new trends
TL;DR: The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems.
Journal ArticleDOI
Entropy for intuitionistic fuzzy sets
Eulalia Szmidt,Janusz Kacprzyk +1 more
TL;DR: It is shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .