Institute of Information Theory and Automation

Publication details

I-Fuzzy equivalence relations and I-fuzzy partitions

Journal Article

Mesiar Radko, Jayaram B.


serial: Information Sciences vol.179, 9 (2009), p. 1278-1297

research: CEZ:AV0Z10750506

project(s): GA402/08/0618, GA ČR

keywords: Conjunctor, Fuzzy equivalence relation, Fuzzy partition, Implicator, Semi-copula

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abstract (eng):

A T-fuzzy equivalence relation is a fuzzy binary relation on a set X which is reflexive, symmetric and T-transitive for a t-norm T. In this work, we eploy a related form of C-transitivity, viz., I-transitivity, where I is an implicator. We show that although every I-fuzzy equivalence relation can be shown to be a C-fuzzy equivalence relation, there exist C-fuzzy equivalence relations that are not I-fuzzy equivalence relations and hence these concepts are not equivalent.

abstract (cze):

Relace T-fuzzy ekvivalence je binární fuzzy relace na množině X, která je reflexivní, symetrická a T-tranzitivní pro t-normu T. V práci jsme zavedli tzv. I-transitivitu, související s C-tranzitivitou, kde I je implikátor. Ukázali jsme, že zatím co každá I-fuzzy relace ekvivalencí je i C-fuzzy relace ekvivalencí, existuje C-fuzzy relace ekvivalencí, která není I-fuzzy relace ekvivalencí a tedy tyto dva přístupy nejsou ekvivalentní.

RIV: BA

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Last modification: 21.12.2012
Institute of Information Theory and Automation