Berhanu Assaye Alaba
Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia

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Journal : International Journal of Computing Science and Applied Mathematics

The Fuzzy Lattice of Ideals and Filters of an Almost Distributive Fuzzy Lattice Berhanu Assaye Alaba; Bekalu Tarekegn Bitew
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 3, No 1 (2017)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (85.286 KB) | DOI: 10.12962/j24775401.v3i1.2113

Abstract

In this paper, the concept of fuzzy lattice is discussed. It is proved that a fuzzy poset (IA(L),B) and (FA(L),B) forms a fuzzy lattice, where IA(L) and FA(L) are the set containing all ideals, and the set containing all filters of an Almost Distributive Fuzzy Lattice(ADFL) respectively. In addition we proved that, a fuzzy poset (PIA(L),B) and (PFA(L),B) forms fuzzy distributive lattice, where PIA and PFA(L) denotes the set containing all principal ideals and the set containing all principal filters of an ADFL. Finally, it is proved that for any ideal I and filter F of an ADFL, IiA = {(i]A : i in I} and FfA = {[f)A : f in F} are ideals of a fuzzy distributive lattice (PIA(L),B) and (PFA(L),B) respectively, and FiA = {(f]A : f in F} and IfA = {[i)A : i in I} are filters of a distributive fuzzy lattice (PIA(L),B) and (PFA(L),B) respectively.
L-Fuzzy Filters of a Poset Berhanu Assaye Alaba; Mihret Alamneh; Derso Abeje
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 5, No 1 (2019)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (197.752 KB) | DOI: 10.12962/j24775401.v5i1.3779

Abstract

Many generalizations of ideals and filters of a lattice to an arbitrary poset have been studied by different scholars. The authors of this paper introduced several generalizations of L-fuzzy ideal of a lattice to an arbitrary poset in [1]. In this paper, we introduce several L-fuzzy filters of a poset which generalize the L-fuzzy filter of a lattice and give several characterizations of them.