L-Normal fuzzy filters of a distributive lattice

In this paper, we study the concept of L-normal fuzzy filters of distributive lattices in terms of annulates. We also study the special class of fuzzy filters called L-normal fuzzy filters. Further, a set of equivalent conditions are derived for an L -fuzzy filter to be an L -normal fuzzy filter, which leads to a characterization of disjunctive lattices. We observe that every L-normal fuzzy filter is the intersection of all L-prime normal fuzzy filters containing it. Finally, we study the space of L -prime normal fuzzy filters and investigate some of their properties.

Keywords:

Distributive lattice , normal filter , L-fuzzy filter , L-normal fuzzy filter , L-prime normal fuzzy filter