Elsevier

Fuzzy Sets and Systems

Volume 133, Issue 2, 16 January 2003, Pages 137-153
Fuzzy Sets and Systems

On (un)suitable fuzzy relations to model approximate equality

https://doi.org/10.1016/S0165-0114(02)00239-7Get rights and content

Abstract

In this paper we state that fuzzy equivalence relations in general are not suitable to model approximate equality, since then the notion of transitivity is counter-intuitive. To substantiate this we investigate some of the undesirable results caused by transitivity, among other things in the case of approximate reasoning. We then introduce a new framework to model approximate equality, i.e. the concept of a pseudometric based resemblance relation. We go into the properties of this new kind of fuzzy relation and illustrate it by means of some examples.

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    Citation Excerpt :

    It is now a well established fact that Fuzzy logic [28] presents a natural approach to deal with vagueness, since it does not require a predicate to be necessarily true or false; rather, it can be true to a certain degree. In the framework of fuzzy set theory, the emergence of the notion of T-transitive relations raised the hope to resolve the paradox of approximate equality [22,29], but unfortunately it did not work (see [5,12,13]). In this scenario, the notion of ϵ-fuzzy transitivity was introduced by Beg and Ashraf [3] to get a better model for approximate equality.

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