L-Normal fuzzy filters of a distributive lattice

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 485-493
  • Receive Date: 23 July 2022
  • Revise Date: 27 September 2022
  • Accept Date: 10 October 2022