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 |
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article-2113 |
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| fullrecord |
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<dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><title lang="en-US">The Fuzzy Lattice of Ideals and Filters of an Almost Distributive Fuzzy Lattice</title><creator>Alaba, Berhanu Assaye; Department of Mathematics, College of Science,
Bahir Dar University, Bahir Dar, Ethiopia</creator><creator>Bitew, Bekalu Tarekegn; Department of Mathematics, College of Science,
Bahir Dar University, Bahir Dar, Ethiopia</creator><subject lang="en-US">Almost distributive fuzzy lattice; filters; fuzzy lattice; ideals</subject><description lang="en-US">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.</description><publisher lang="en-US">Institut Teknologi Sepuluh Nopember</publisher><contributor lang="en-US"/><date>2017-03-01</date><type>Journal:Article</type><type>Other:info:eu-repo/semantics/publishedVersion</type><type>Journal:Article</type><type>File:application/pdf</type><identifier>http://iptek.its.ac.id/index.php/ijcsam/article/view/2113</identifier><identifier>10.12962/j24775401.v3i1.2113</identifier><source lang="en-US">International Journal of Computing Science and Applied Mathematics; Vol 3, No 1 (2017); 1-4</source><source>2477-5401</source><language>eng</language><relation>http://iptek.its.ac.id/index.php/ijcsam/article/view/2113/1714</relation><rights lang="en-US">International Journal of Computing Science and Applied Mathematics Copyright and consent from  To ensure uniformity of treatment among all contributors, other forms may not be substituted for this form, nor may any wording of the form be changed.  This form is intended for original material submitted to International Journal of Computing Science and Applied Mathematics and must accompany any such material in order to be published by International Journal of Computing Science and Applied Mathematics.  Please read the form carefully and keep a copy for your files. TITLE OF PAPER/ARTICLE/REPORT, INCLUDING ALL CONTENT IN ANY FORM, FORMAT, OR MEDIA:COPYRIGHT TRANSFERThe undersigned hereby assigns to International Journal of Computing Science and Applied Mathematics all rights under copyright that may exist in and to: (a) the above Work, including any revised or expanded derivative works submitted to International Journal of Computing Science and Applied Mathematics by the undersigned based on the Work; 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|
| language |
eng |
| format |
Journal:Article Journal Other:info:eu-repo/semantics/publishedVersion Other File:application/pdf File Journal:eJournal |
| author |
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 |
| title |
The Fuzzy Lattice of Ideals and Filters of an Almost Distributive Fuzzy Lattice |
| publisher |
Institut Teknologi Sepuluh Nopember |
| publishDate |
2017 |
| topic |
Almost distributive fuzzy lattice filters fuzzy lattice ideals |
| url |
http://iptek.its.ac.id/index.php/ijcsam/article/view/2113 http://iptek.its.ac.id/index.php/ijcsam/article/view/2113/1714 |
| contents |
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. |
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