Μ-Fuzzy Filters in Distributive Lattices. (29th December 2020)

• Record Type: Journal Article
• Authors: Norahun, Wondwosen Zemene
• Other Names: Dvorák Antonin Academic Editor.
• Is Part Of: Advances in fuzzy systems. Volume 2020(2020)
• Publication Date: 2020-12-29
• Subjects: Fuzzy systems -- Periodicals; Systèmes flous; Fuzzy systems; Periodicals; 511.313
• DOI: 10.1155/2020/8841670
• Languages: English
• ISSNs: 1687-7101

Abstract

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 X μ . It is proved that the space X μ is a T 0 space.