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

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