{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:41:12Z","timestamp":1777704072282,"version":"3.51.4"},"reference-count":32,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,11,23]],"date-time":"2019-11-23T00:00:00Z","timestamp":1574467200000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2020,2,6]]},"abstract":"\n \u00a0In this paper, for a non-degenerate convex set\n Y<\/jats:italic>\n in\n R<\/jats:bold>\n \n n<\/jats:italic>\n <\/jats:sup>\n containing\n 0<\/jats:bold>\n , two special function spaces\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n ) and\n E<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n ) which consist of all fuzzy star-shaped numbers and of all fuzzy numbers in\n R<\/jats:bold>\n \n n<\/jats:italic>\n <\/jats:sup>\n with respect to\n 0<\/jats:bold>\n and their supports being included in\n Y<\/jats:italic>\n with the endograph metric\n D<\/jats:italic>\n are investigated. Some conclusions and methods in topology are used to discuss the topological structure of (\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n ) and the pair ((\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n )\u00a0, (\n E<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n )). The main results are as follows: 1. The space (\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n ) is homeomorphic to the Hilbert cube\n Q<\/jats:italic>\n \u00a0=\u00a0[-1, 1]\u00a0\n \n N<\/jats:bold>\n <\/jats:sup>\n if and only if\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n ) is compact if and only if\n Y<\/jats:italic>\n is compact. 2. There exists a homeomorphism\n h<\/jats:italic>\n \u00a0:\u00a0(\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n )\u00a0\u2192\u00a0\n Q<\/jats:italic>\n such that\n h<\/jats:italic>\n \u00a0(\n E<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n ))\u00a0=\u00a0{1}\u00a0\u00d7\u00a0[-1, 1]\u00a0\n \n N<\/jats:bold>\n \\{1}\n <\/jats:sup>\n if\n Y<\/jats:italic>\n is compact but not a segment. 3. The space (\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n )\u00a0,\n D<\/jats:italic>\n ) homeomorphic to the pseudoboundary of the Hilbert cube if and only if\n S<\/jats:italic>\n \n 0<\/jats:bold>\n <\/jats:sub>\n \u00a0(\n Y<\/jats:italic>\n ) is non-compact and\n \u03c3<\/jats:italic>\n -compact if and only if\n Y<\/jats:italic>\n is non-compact and locally compact.\n <\/jats:p>","DOI":"10.3233\/jifs-190272","type":"journal-article","created":{"date-parts":[[2019,11,26]],"date-time":"2019-11-26T11:04:23Z","timestamp":1574766263000},"page":"1855-1864","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["A special fuzzy star-shaped numbers space with endograph metric"],"prefix":"10.1177","volume":"38","author":[{"given":"Hanbiao","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China P.R."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daocheng","family":"Zeng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shantou University, Guangdong, China P.R."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,11,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90319-Y"},{"key":"e_1_3_2_3_2","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1307\/mmj\/1029003410","article-title":"Characterizing certain incomplete infinite-dimensional absolute retracts","volume":"33","author":"Bestvina M.","year":"1986","unstructured":"BestvinaM., MogilskiJ., Characterizing certain incomplete infinite-dimensional absolute retracts, The Michigan Mathematical Journal 33 (1986), 291\u2013313.","journal-title":"The Michigan Mathematical Journal"},{"key":"e_1_3_2_4_2","unstructured":"BoydS. 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