L-Normal fuzzy filters of a distributive lattice

Norahun, Wondwosen Zemene; Mulat Addis, Gezahagne; Alemayehu, Teferi Getachew; Boku, Dereje Kifle

doi:10.22075/ijnaa.2022.27889.3748

L-Normal fuzzy filters of a distributive lattice

Document Type : Research Paper

Authors

Wondwosen Zemene Norahun ¹

Gezahagne Mulat Addis ¹

Teferi Getachew Alemayehu ²

Dereje Kifle Boku ³

¹ Department of Mathematics, University of Gondar, Gondar, Ethiopia

² Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia

³ Department of Mathematics, Dilla University, Dilla, Ethiopia

10.22075/ijnaa.2022.27889.3748

Abstract

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