{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:41:31Z","timestamp":1777704091187,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T00:00:00Z","timestamp":1595548800000},"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":[[2020,10,7]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>D<\/jats:italic>\n                    be a finite distributive lattice with\n                    <jats:italic>n<\/jats:italic>\n                    join-irreducible elements. It is well-known that\n                    <jats:italic>D<\/jats:italic>\n                    can be represented as the congruence lattice of a rectangular lattice\n                    <jats:italic>L<\/jats:italic>\n                    which is a special planer semimodular lattice. In this paper, we shall give a better upper bound for the size of\n                    <jats:italic>L<\/jats:italic>\n                    by a function of\n                    <jats:italic>n<\/jats:italic>\n                    , improving a 2009 result of G. Gr\u00e4tzer and E. Knapp.\n                  <\/jats:p>","DOI":"10.3233\/jifs-191220","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T15:21:19Z","timestamp":1595949679000},"page":"2831-2843","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Congrunce lattices of rectangular lattices"],"prefix":"10.1177","volume":"39","author":[{"given":"Peng","family":"He","sequence":"first","affiliation":[{"name":"College of Applied Mathematics, Chengdu University of Information Technology Chengdu, Sichuan People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-Ping","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,7,24]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"EarnshawB.A. Combinatorial aspects of partially ordered sets (Lecture notes) http:\/\/users.math.msu.edu\/users\/earnshaw\/research\/poset.pdf (2005)."},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-013-0264-x"},{"key":"e_1_3_1_4_2","doi-asserted-by":"crossref","unstructured":"Gr\u00e4tzerG. 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Lattice theory: special topics and applications Birkh\u00e4user Basel 2014.","DOI":"10.1007\/978-3-319-06413-0"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-191220","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-191220","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-191220","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:22Z","timestamp":1777455622000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-191220"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,10,7]]}},"alternative-id":["10.3233\/JIFS-191220"],"URL":"https:\/\/doi.org\/10.3233\/jifs-191220","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,24]]}}}