Journal ArticleDOI
Twofold fuzzy sets and rough sets—Some issues in knowledge representation
Didier Dubois,Henri Prade +1 more
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The notion of twofold fuzzy sets was introduced in this article, where the relevant information for determining the membership status is incomplete and the notion of fuzzy sets are used to represent sets where the membership of some elements may be ill-known rather than just a matter of degree.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1987-07-01. It has received 209 citations till now. The article focuses on the topics: Fuzzy set operations & Type-2 fuzzy sets and systems.read more
Citations
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Journal ArticleDOI
Rough fuzzy sets and fuzzy rough sets
Didier Dubois,Henri Prade +1 more
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
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
Rudiments of rough sets
Zdziasław Pawlak,Andrzej Skowron +1 more
TL;DR: The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.
Book ChapterDOI
Putting Rough Sets and Fuzzy Sets Together
Didier Dubois,Henri Prade +1 more
TL;DR: It is argued that fuzzy sets and rough sets aim to different purposes and that it is more natural to try to combine the two models of uncertainty (vagueness for fuzzy set and coarseness for rough sets) in order to get a more accurate account of imperfect information.
Journal ArticleDOI
A decision theoretic framework for approximating concepts
Yiyu Yao,S. K. M. Wong +1 more
TL;DR: This paper shows that if a given concept is approximated by one set, the same result given by the α-cut in the fuzzy set theory is obtained, and can derive both the algebraic and probabilistic rough set approximations.
References
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Book
A mathematical theory of evidence
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Journal ArticleDOI
Intuitionistic fuzzy sets
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Journal ArticleDOI
Fuzzy sets as a basis for a theory of possibility
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Intuitionistic Fuzzy Sets
TL;DR: In this article, a definition of the concept "intuitionistic fuzzy set" (IFS) is given, the latter being a generalization of the Fuzzy Set and an example is described.