{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:40:15Z","timestamp":1747190415754,"version":"3.40.5"},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T00:00:00Z","timestamp":1609200000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2020,12,29]]},"abstract":"<jats:p>In this paper, we introduce the concept of <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <a:mi>\u03bc<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula>-fuzzy filters in distributive lattices. We study the special class of fuzzy filters called <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <c:mi>\u03bc<\/c:mi>\n                     <\/c:math>\n                  <\/jats:inline-formula>-fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <e:mi>\u03bc<\/e:mi>\n                     <\/e:math>\n                  <\/jats:inline-formula>-fuzzy filter is the intersection of all prime <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <g:mi>\u03bc<\/g:mi>\n                     <\/g:math>\n                  <\/jats:inline-formula>-fuzzy filters containing it. We also topologize the set of all prime <jats:inline-formula>\n                     <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <i:mi>\u03bc<\/i:mi>\n                     <\/i:math>\n                  <\/jats:inline-formula>-fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of <jats:inline-formula>\n                     <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <k:mi>\u03bc<\/k:mi>\n                     <\/k:math>\n                  <\/jats:inline-formula>-fuzzy filters and the lattice of all open sets in <jats:inline-formula>\n                     <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <m:msub>\n                           <m:mrow>\n                              <m:mi>X<\/m:mi>\n                           <\/m:mrow>\n                           <m:mrow>\n                              <m:mi>\u03bc<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:msub>\n                     <\/m:math>\n                  <\/jats:inline-formula>. It is proved that the space <jats:inline-formula>\n                     <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <o:msub>\n                           <o:mrow>\n                              <o:mi>X<\/o:mi>\n                           <\/o:mrow>\n                           <o:mrow>\n                              <o:mi>\u03bc<\/o:mi>\n                           <\/o:mrow>\n                        <\/o:msub>\n                     <\/o:math>\n                  <\/jats:inline-formula> is a <jats:inline-formula>\n                     <q:math xmlns:q=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\">\n                        <q:msub>\n                           <q:mrow>\n                              <q:mi>T<\/q:mi>\n                           <\/q:mrow>\n                           <q:mrow>\n                              <q:mn>0<\/q:mn>\n                           <\/q:mrow>\n                        <\/q:msub>\n                     <\/q:math>\n                  <\/jats:inline-formula> space.<\/jats:p>","DOI":"10.1155\/2020\/8841670","type":"journal-article","created":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T17:36:03Z","timestamp":1609263363000},"page":"1-9","source":"Crossref","is-referenced-by-count":6,"title":["<a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mi>\u03bc<\/a:mi>\n                  <\/a:math>-Fuzzy Filters in Distributive Lattices"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6673-9914","authenticated-orcid":true,"given":"Wondwosen Zemene","family":"Norahun","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Gondar, Gondar, Ethiopia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1215\/S0012-7094-70-03748-8","article-title":"Relative annihilators in lattices","volume":"37","author":"M. 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