Paper Info
Title
A similarity-based generalization of fuzzy orderings preserving the classical axioms
Abstract
Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging far behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studied in detail, including several constructions and representation results.
Year
DOI
Venue
2000
10.1142/S0218488500000411
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Keywords
Field
DocType
similarity-based generalization,fuzzy ordering,— fuzzy equivalence relation,fuzzy relation.,classical axiom,fuzzy control,fuzzy set theory,equivalence relation
Discrete mathematics,Defuzzification,Fuzzy classification,Fuzzy set operations,Fuzzy measure theory,Fuzzy mathematics,Fuzzy subalgebra,Type-2 fuzzy sets and systems,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
8
5
0218-4885
Citations 
PageRank 
References 
63
8.11
2
Authors
1
Name
Order
Citations
PageRank
Ulrich Bodenhofer170568.02