On (un)suitable fuzzy relations to model approximate equality

Authors:
Martine De Cock;Etienne Kerre
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 291 (S9), B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 291 (S9), B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems - Theme: Basic notions
Year:
2003

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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.