{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:53:36Z","timestamp":1777704816959,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T00:00:00Z","timestamp":1589846400000},"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":[[2020,7,17]]},"abstract":"<jats:p>\n                    \u00a0For a fuzzy subset system\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    , the concepts of a\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    -completion and a\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    -completion of a given fuzzy poset (\n                    <jats:italic>X<\/jats:italic>\n                    ,\n                    <jats:italic>e<\/jats:italic>\n                    ) are introduced and their universal properties are investigated. In this paper, we prove that: (1) the\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    -completion\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    \u00a0(\n                    <jats:italic>X<\/jats:italic>\n                    ) is a join-completion with the universal property; (2) the\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    -completion\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    \u00a0(\n                    <jats:italic>X<\/jats:italic>\n                    ) is the smallest\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    -complete fuzzy subposet of\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    \u00a0(\n                    <jats:italic>X<\/jats:italic>\n                    ) in the case that\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>L<\/jats:italic>\n                    <\/jats:sub>\n                    is fuzzy subset-hereditary. The results show that the Dedekind-MacNeille completion is a special case of the\n                    <jats:italic>Z<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>\u0393<\/jats:italic>\n                      <jats:sub>\n                        <jats:italic>L<\/jats:italic>\n                      <\/jats:sub>\n                    <\/jats:sub>\n                    -completion.\n                  <\/jats:p>","DOI":"10.3233\/jifs-200121","type":"journal-article","created":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T12:49:22Z","timestamp":1589892562000},"page":"1347-1359","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["The\n                    <i>Z<\/i>\n                    <sub>\n                      <i>L<\/i>\n                    <\/sub>\n                    -completions of fuzzy posets"],"prefix":"10.1177","volume":"39","author":[{"given":"Shuhua","family":"Su","sequence":"first","affiliation":[{"name":"School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Songjiang, Shanghai, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuqun","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Songjiang, Shanghai, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Li","sequence":"additional","affiliation":[{"name":"Fuzhou Teachers\u2019 College, East China University of Technology, Fuzhou, Jiangxi, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,5,19]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7456"},{"key":"e_1_3_2_3_2","unstructured":"B\u0115lohl\u00e1vekR. 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