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All Journal International Journal of Computing Science and Applied Mathematics-IJCSAM
Bekalu Tarekegn
Bahir Dar University
Mathematics

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

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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.
Co-Authors Berhanu Assaye Alaba