{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:37:05Z","timestamp":1777703825526,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T00:00:00Z","timestamp":1495497600000},"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":[[2017,5,23]]},"abstract":"\n Four properties of\n M<\/jats:italic>\n -fuzzifying interval spaces, namely,\n M<\/jats:italic>\n -fuzzifying geometric property,\n M<\/jats:italic>\n -fuzzifying modular property,\n M<\/jats:italic>\n -fuzzifying Pasch property and\n M<\/jats:italic>\n -fuzzifying sand-glass property, are introduced and characterized. Those properties together with\n M<\/jats:italic>\n -fuzzifying Peano property and\n M<\/jats:italic>\n -fuzzifying JHC property are closely related to each other. For example, an\n M<\/jats:italic>\n -fuzzifying idempotent Peano-Pasch interval operator possesses\n M<\/jats:italic>\n -fuzzifying geometric property and\n M<\/jats:italic>\n -fuzzifying sand-glass property. In addition, in an\n M<\/jats:italic>\n -fuzzifying modular space,\n M<\/jats:italic>\n -fuzzifying Peano property,\n M<\/jats:italic>\n -fuzzifying Pasch property,\n M<\/jats:italic>\n -fuzzifying geometric property and\n M<\/jats:italic>\n -fuzzifying sand-glass property combined with JHC property are equivalent.\n <\/jats:p>","DOI":"10.3233\/jifs-16667","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T14:43:23Z","timestamp":1495809803000},"page":"4273-4284","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":29,"title":["Geometric properties of\n M<\/i>\n -fuzzifying convex structures"],"prefix":"10.1177","volume":"32","author":[{"given":"Xiu-Yun","family":"Wu","sequence":"first","affiliation":[{"name":"School of Science, Hunan University of Science and Engineering, Hunan, China"},{"name":"School of Mathematics and Computational Science, Xiangtan University, Hunan, China"}]},{"given":"Er-Qiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, China"}]},{"given":"Shi-Zhong","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science, Wuyi University, Guangdong, China"}]}],"member":"179","published-online":{"date-parts":[[2017,5,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1990.11995655"},{"key":"e_1_3_2_3_2","first-page":"289","article-title":"Geometric convexity, i","volume":"2","author":"Cantwell J.","year":"1974","unstructured":"CantwellJ. and KayD.C., Geometric convexity, i, Bull Inst Math Acad Sinica 2 (1974), 289\u2013307.","journal-title":"Bull Inst Math Acad Sinica"},{"key":"e_1_3_2_4_2","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BF01449883","article-title":"\u00dcber den variabilit\u00e4tsbereich der koeffizienten von potenzreihen","volume":"64","author":"Carath\u00e9odory C.","year":"1907","unstructured":"Carath\u00e9odoryC., \u00dcber den variabilit\u00e4tsbereich der koeffizienten von potenzreihen, Math Ann 64 (1907), 95\u2013115.","journal-title":"Math Ann"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.07.014"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700012417"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.03.003"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1962.11989897"},{"key":"e_1_3_2_9_2","first-page":"175","article-title":"\u00dcber mengen konvexer k\u00f6rper mit geneinschaftlichen punkten","volume":"32","author":"Helly. E.","year":"1923","unstructured":"Helly.E., \u00dcber mengen konvexer k\u00f6rper mit geneinschaftlichen punkten, Jber Deutsch Mat Verein 32 (1923), 175\u2013176.","journal-title":"Jber Deutsch Mat Verein"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.5802\/afst.766"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(77)90233-5"},{"key":"e_1_3_2_12_2","unstructured":"KubisW. Abstract convex structures in topology and set theory. PhD thesis University of Silesia Katowice Poland 1999."},{"key":"e_1_3_2_13_2","first-page":"65","article-title":"On helly\u2019s theorem and the axioms of convexity","volume":"15","author":"Levi F.W.","year":"1951","unstructured":"LeviF.W., On helly\u2019s theorem and the axioms of convexity, J Indian Math Soc 15 (1951), 65\u201376.","journal-title":"J Indian Math Soc"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/0233193021000015587"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.5918"},{"key":"e_1_3_2_16_2","first-page":"22","article-title":"Lattice-valued fuzzy convex geometry","volume":"164","author":"Maruyama Y.","year":"2009","unstructured":"MaruyamaY., Lattice-valued fuzzy convex geometry, Optimization 164 (2009), 22\u201337.","journal-title":"Optimization"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90199-1"},{"key":"e_1_3_2_18_2","first-page":"229","article-title":"On the convexity of sets","volume":"40","author":"Nachbin L.","year":"1992","unstructured":"NachbinL., On the convexity of sets, Acad Sci Math 40 (1992), 229\u2013234.","journal-title":"Acad Sci Math"},{"key":"e_1_3_2_19_2","article-title":"Subcategories of the category of L-convex spaces","author":"Pang B.","year":"2016","unstructured":"PangB. and ShiF.G., Subcategories of the category of L-convex spaces, Fuzzy Sets Syst (2016). (Accepted) DOI: 10.1016\/j.fss.2016.02.014","journal-title":"Fuzzy Sets Syst"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1080\/02331939708844289"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9438-9"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01464231"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940467"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90076-0"},{"key":"e_1_3_2_25_2","first-page":"65","article-title":"Theory of L\n \n \u03b2\n -nested sets and L\n \n \u03b1\n -nested sets and its applications","volume":"9","author":"Shi F.G.","year":"1999","unstructured":"ShiF.G., Theory of L\u03b2-nested sets and L\u03b1-nested sets and its applications, Fuzzy Syst Math 9 (1999), 65\u201372. (in chinese).","journal-title":"Fuzzy Syst Math"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.09.002"},{"key":"e_1_3_2_27_2","first-page":"231","article-title":"-fuzzy metric spaces","volume":"52","author":"Shi F.G.","year":"2010","unstructured":"ShiF.G., -fuzzy metric spaces, Indian J Math 52 (2010), 231\u2013250.","journal-title":"Indian J Math"},{"key":"e_1_3_2_28_2","first-page":"127","article-title":"Categories isomorphic to the category of L-fuzzy closure system spaces","volume":"5","author":"Shi F.G.","year":"2013","unstructured":"ShiF.G. and PangB., Categories isomorphic to the category of L-fuzzy closure system spaces, Iran J Fuzzy Syst 5 (2013), 127\u2013146.","journal-title":"Iran J Fuzzy Syst"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151765"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/249183"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-48.1.1"},{"key":"e_1_3_2_32_2","volume-title":"Theory of Convex Structures","author":"van de Vel M.L.J.","year":"1993","unstructured":"van de VelM.L.J., Theory of Convex Structures. Noth-Holland, New-York, 1993."},{"key":"e_1_3_2_33_2","volume-title":"Theory of L-fuzzy Topological Spaces","author":"Wang G.J.","year":"1988","unstructured":"WangG.J., Theory of L-fuzzy Topological Spaces. Shanxi Normal University Press, Xi\u2019an, 1988. (in chinese)."},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90301-J"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-152015"},{"key":"e_1_3_2_36_2","unstructured":"XiuZ.Y. Studies on (L M)-fuzzy convexity spaces and related theory. PhD thesis Beijing institute of Technology Beijing China 2015. (in chinese)."},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90100-5"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.01.007"}],"container-title":["Journal of Intelligent & Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16667","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-16667","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16667","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:42Z","timestamp":1777455582000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-16667"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,23]]},"references-count":37,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,5,23]]}},"alternative-id":["10.3233\/JIFS-16667"],"URL":"https:\/\/doi.org\/10.3233\/jifs-16667","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,23]]}}}