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
