The Fuzzy Lattice of Ideals and Filters of an Almost Distributive Fuzzy Lattice
| Main Authors: | Alaba, Berhanu Assaye; Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia, Bitew, Bekalu Tarekegn; Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Institut Teknologi Sepuluh Nopember
, 2017
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| Subjects: | |
| Online Access: |
http://iptek.its.ac.id/index.php/ijcsam/article/view/2113 http://iptek.its.ac.id/index.php/ijcsam/article/view/2113/1714 |
Daftar Isi:
- 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.