Journal ArticleDOI
Fuzzy partitions and relations; an axiomatic basis for clustering
James C. Bezdek,J Douglas Harris +1 more
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A new definition of transitivity for fuzzy relations yields a relation-theoretic characterization of the class of all psuedo-metrics on a fixed data set into the closed unit interval.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1978-04-01. It has received 339 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.read more
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Book
Fuzzy Set Theory - and Its Applications
TL;DR: The book 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.
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 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
Fuzzy set theory
TL;DR: In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques.
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A survey of fuzzy clustering
TL;DR: A survey of fuzzy set theory applied in cluster analysis in three categories: the fuzzy clustering based on fuzzy relation, the fuzzy generalized k-nearest neighbor rule, and an overview of a nonparametric classifier.
References
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Journal ArticleDOI
Pattern Classification and Scene Analysis.
Book
Pattern classification and scene analysis
Richard O. Duda,Peter E. Hart +1 more
TL;DR: In this article, a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition is provided, including Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.
Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Journal ArticleDOI
A new approach to clustering
TL;DR: A new method of representation of the reduced data, based on the idea of “fuzzy sets,” is proposed to avoid some of the problems of current clustering procedures and to provide better insight into the structure of the original data.
Journal ArticleDOI
Pattern Classification Based on Fuzzy Relations
TL;DR: A method of classifying patterns using fuzzy relations is described, where a similitude between any two patterns is calculated by using the composition of a fuzzy relation to induce an equivalence relation.