{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:31:54Z","timestamp":1777703514207,"version":"3.51.4"},"reference-count":18,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T00:00:00Z","timestamp":1562544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,9,9]]},"abstract":"<jats:p>\n                    In this paper, we introduce the co-annihilator\n                    <jats:sup>\u22a5<\/jats:sup>\n                    <jats:italic>A<\/jats:italic>\n                    of a set\n                    <jats:italic>A<\/jats:italic>\n                    and the co-annihilator of (\n                    <jats:italic>F<\/jats:italic>\n                    \u00a0:\u00a0\n                    <jats:italic>a<\/jats:italic>\n                    ) of\n                    <jats:italic>a<\/jats:italic>\n                    relative to a prefilter (filter)\n                    <jats:italic>F<\/jats:italic>\n                    in an EQ-algebra\n                    <jats:italic>\u025b<\/jats:italic>\n                    . We investigate related properties of them, and obtain that the lattice of all prefilters\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">PF<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>\u025b<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    forms a pseudo-complemented lattice and the collection of all co-annihilators\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">COA<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>\u025b<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    forms a Boolean algebra in a separated EQ-algebra\n                    <jats:italic>\u025b<\/jats:italic>\n                    . Moreover, we introduce the notion of \u0394-co-annihilators in an EQ\n                    <jats:sub>\u0394<\/jats:sub>\n                    -algebra\n                    <jats:italic>\u025b<\/jats:italic>\n                    <jats:sub>\u0394<\/jats:sub>\n                    and conclude that the collection of all \u0394-prefilters\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi mathvariant=\"script\">PF<\/mml:mi>\n                          <mml:mi>\u0394<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:msub>\n                          <mml:mi>\u025b<\/mml:mi>\n                          <mml:mi>\u0394<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    in an \u2113EQ\n                    <jats:sub>\u0394<\/jats:sub>\n                    -algebra\n                    <jats:italic>\u025b<\/jats:italic>\n                    <jats:sub>\u0394<\/jats:sub>\n                    constitutes a relative pseudo-complemented lattice. Finally, we introduce and investigate two types of fuzzy co-annihilators\n                    <jats:italic>Ann<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>R<\/jats:italic>\n                    <\/jats:sub>\n                    \u00a0(\n                    <jats:italic>\u03bc<\/jats:italic>\n                    ) and\n                    <jats:italic>Ann<\/jats:italic>\n                    \u00a0(\n                    <jats:italic>\u03bc<\/jats:italic>\n                    ,\n                    <jats:italic>\u03bd<\/jats:italic>\n                    ) in\n                    <jats:italic>\u025b<\/jats:italic>\n                    . We come to a conclusion that the set of all fuzzy filters\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">FF<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>\u025b<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    in a residuated \u2113EQ-algebra\n                    <jats:italic>\u025b<\/jats:italic>\n                    forms a relative pseudo-complemented lattice whence \u2192 is the G\u00f6del residuated implication in\n                    <jats:italic>St<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>r<\/jats:italic>\n                    <\/jats:sup>\n                    \u00a0(\n                    <jats:italic>\u03bc<\/jats:italic>\n                    ,\n                    <jats:italic>\u03bd<\/jats:italic>\n                    ).\n                  <\/jats:p>","DOI":"10.3233\/jifs-179373","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T14:00:48Z","timestamp":1562940048000},"page":"2113-2124","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Co-annihilators and fuzzy co-annihilators in EQ-algebras"],"prefix":"10.1177","volume":"37","author":[{"given":"Xiaoyun","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an Aeronautical University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arsham Borumand","family":"Saeid","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoli","family":"He","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Shiyou University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,7,8]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"BlythT.S. 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