Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214120230101L-Normal fuzzy filters of a distributive lattice485493702310.22075/ijnaa.2022.27889.3748ENWondwosen ZemeneNorahunDepartment of Mathematics, University of Gondar, Gondar, Ethiopia0000-0001-6673-9914Gezahagne Mulat AddisDepartment of Mathematics, University of Gondar, Gondar, Ethiopia0000-0002-6735-6832Teferi GetachewAlemayehuDepartment of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia0000-0001-9832-9522Dereje KifleBokuDepartment of Mathematics, Dilla University, Dilla, EthiopiaJournal Article20220723In 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.https://ijnaa.semnan.ac.ir/article_7023_49aad77d83638c45d8d4997fd93aad9b.pdf