On the fuzzy pseudo ordered sets

Abstract

In this thesis, we study the notion of fuzzy pseudo ordered sets and some of its interesting properties, and then we introduce the concept of fuzzy trellis as a natural generalization of the trellis introduced by Skala with respect to a fuzzy pseudo order relation. In addition, we introduce the notion of fuzzy ideal (resp. fuzzy filter) as fuzzy sets on a crisp trellis and we present interesting characterizations of these notions. We pay particular attention to the principal fuzzy ideals (resp. filters) on a given trellis, which is more complicated than the same notions on a lattice. At the end, we provide various characterizations of intuitionistic fuzzy ideals (resp. fuzzy filters) on a lattice