{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:22:06Z","timestamp":1777702926348,"version":"3.51.4"},"reference-count":43,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T00:00:00Z","timestamp":1554940800000},"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":[[2019,4,11]]},"abstract":"<jats:p>\n                    In this paper, we generalize a series of research work about convexity on classical partially ordered sets to fuzzy partially ordered sets (\n                    <jats:italic>L<\/jats:italic>\n                    -posets). Taking a complete Heyting algebra as the truth value structure, we propose an\n                    <jats:italic>L<\/jats:italic>\n                    -ordered\n                    <jats:italic>L<\/jats:italic>\n                    -convex structure on an\n                    <jats:italic>L<\/jats:italic>\n                    -poset and give its corresponding\n                    <jats:italic>L<\/jats:italic>\n                    -convex hulls. We characterize the\n                    <jats:italic>L<\/jats:italic>\n                    -ordered\n                    <jats:italic>L<\/jats:italic>\n                    -convex sets in terms of four kinds of cut sets of\n                    <jats:italic>L<\/jats:italic>\n                    -subsets, and discuss the product of\n                    <jats:italic>L<\/jats:italic>\n                    -ordered\n                    <jats:italic>L<\/jats:italic>\n                    -convex sets. We also discuss\n                    <jats:italic>L<\/jats:italic>\n                    -convexity-preserving (resp.,\n                    <jats:italic>L<\/jats:italic>\n                    -convex-to-convex) mappings. After that, with a consideration of the degree to which an\n                    <jats:italic>L<\/jats:italic>\n                    -subset is an\n                    <jats:italic>L<\/jats:italic>\n                    -ordered\n                    <jats:italic>L<\/jats:italic>\n                    -convex set, an\n                    <jats:italic>L<\/jats:italic>\n                    -ordered (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>L<\/jats:italic>\n                    )-fuzzy convex structure is introduced. The properties such as equivalent descriptions, the product and (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>L<\/jats:italic>\n                    )-fuzzy convexity-preserving mappings are analyzed.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18170","type":"journal-article","created":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T10:39:55Z","timestamp":1555065595000},"page":"3607-3617","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Convexity on fuzzy partially ordered sets"],"prefix":"10.1177","volume":"36","author":[{"given":"Hongping","family":"Liu","sequence":"first","affiliation":[{"name":"School of Science, Shandong Jianzhu University, Jinan, P.R.China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Shandong Jianzhu 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