Properties of interval-valued fuzzy relations, Atanassov's operators and decomposable operations

Abstract

In this paper we study properties of interval-valued fuzzy relations which were introduced by L.A. Zadeh in 1975. Fuzzy set theory turned out to be a useful tool to describe situations in which the data are imprecise or vague. Interval-valued fuzzy set theory is a generalization of fuzzy set theory which was introduced also by Zadeh in 1965. We examine some properties of interval-valued fuzzy relations in the context of Atanassov's operators and decomposable operations in interval-valued fuzzy set theory. © Springer-Verlag Berlin Heidelberg 2010.