μ-Fuzzy Filters in Distributive Lattices

Abstract

In this paper, we introduce the concept of μ-fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ-fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ-fuzzy filter is the intersection of all prime μ-fuzzy filters containing it. We also topologize the set of all prime μ-fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of μ-fuzzy filters and the lattice of all open sets in Xμ. It is proved that the space Xμ is a T0 space.