Poset valued intuitionistic fuzzy sets

Abstract

In this paper poset valued intuitionistic fuzzy sets are introduced and investigated (for posets in general). It is proved that in case of arbitrary finite posets, represented as a poset of a convenient distributive lattice, a natural version of the definition is obtained, using join-irreducible elements. Two families of cuts and their properties are investigated. Necessary and sufficient conditions under which two families of subsets are families of cuts of a poset valued intuitionistic fuzzy set are given.