{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T22:04:05Z","timestamp":1776377045342,"version":"3.51.2"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771263"],"award-info":[{"award-number":["11771263"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010228","name":"Natural Science Foundation of Shaanxi Provincial Department of Education","doi-asserted-by":"publisher","award":["18JK0360"],"award-info":[{"award-number":["18JK0360"]}],"id":[{"id":"10.13039\/501100010228","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s40314-021-01690-5","type":"journal-article","created":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T09:03:45Z","timestamp":1636707825000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Concave (L,\u00a0M)-fuzzy interior operators and (L,\u00a0M)-fuzzy hull operators"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3094-1210","authenticated-orcid":false,"given":"Hu","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xia","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O. R.","family":"Sayed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"El-Sanousy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y. H. Ragheb","family":"Sayed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,12]]},"reference":[{"key":"1690_CR1","volume-title":"Abstract and concrete categories","author":"J Ad\u00e1amek","year":"1990","unstructured":"Ad\u00e1amek J, Herrlich H, Strecker GE (1990) Abstract and concrete categories. Wiley, New York"},{"key":"1690_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0022-247X(67)90189-8","volume":"18","author":"JA Goguen","year":"1967","unstructured":"Goguen JA (1967) $$L$$-fuzzy sets. J Math Anal Appl 18:145\u2013174","journal-title":"J Math Anal Appl"},{"issue":"1","key":"1690_CR3","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1186\/s40064-016-3255-5","volume":"5","author":"Q Jin","year":"2016","unstructured":"Jin Q, Li L-Q (2016) On the embedding of $$L$$-convex spaces in stratified L-convex spaces. SpringerPlus 5(1):1610","journal-title":"SpringerPlus"},{"key":"1690_CR4","first-page":"969","volume":"25","author":"M Lassak","year":"1977","unstructured":"Lassak M (1977) On metric $$B$$-convexity for which diameters of any set and its hull are equal. Bull Acad Pol Sci Ser Sci Math Astron Phys 25:969\u2013975","journal-title":"Bull Acad Pol Sci Ser Sci Math Astron Phys"},{"key":"1690_CR5","doi-asserted-by":"publisher","first-page":"3209","DOI":"10.3233\/JIFS-161491","volume":"33","author":"LQ Li","year":"2017","unstructured":"Li LQ (2017) On the category of enriched $$(L, M)$$-convex spaces. J Intell Fuzzy Syst 33:3209\u20133216","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR6","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.fss.2018.05.008","volume":"350","author":"E Li","year":"2018","unstructured":"Li E, Shi F-G (2018) Some properties of $$M$$-fuzzifying convexities induced by $$M$$-orders. Fuzzy Sets Syst 350:41\u201354","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"1690_CR7","doi-asserted-by":"publisher","first-page":"2265","DOI":"10.3233\/JIFS-182569","volume":"37","author":"Q-H Li","year":"2019","unstructured":"Li Q-H, Huang H-L, Xiu Z-Y (2019) Degrees of special mappings in the theory of $$L$$-convex spaces. J Intell Fuzzy Syst 37(2):2265\u20132274","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR8","volume-title":"Fuzzy topology","author":"Y-M Liu","year":"1997","unstructured":"Liu Y-M, Luo M-K (1997) Fuzzy topology. World Scientific Publishing, Singapore"},{"key":"1690_CR9","first-page":"22","volume":"1641","author":"Y Maruyama","year":"2009","unstructured":"Maruyama Y (2009) Lattice-valued fuzzy convex geometry. RIMS Kokyuroku 1641:22\u201337","journal-title":"RIMS Kokyuroku"},{"issue":"11","key":"1690_CR10","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.2989\/16073606.2019.1637379","volume":"43","author":"B Pang","year":"2020","unstructured":"Pang B (2020) Convergence structures in $$M$$-fuzzifying convex spaces. Quaest Math 43(11):1541\u20131561","journal-title":"Quaest Math"},{"key":"1690_CR11","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.fss.2016.02.014","volume":"313","author":"B Pang","year":"2017","unstructured":"Pang B, Shi F-G (2017) Subcategories of the category of $$L$$-convex spaces. Fuzzy Sets Syst 313:61\u201374","journal-title":"Fuzzy Sets Syst"},{"issue":"8","key":"1690_CR12","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.2989\/16073606.2018.1436613","volume":"41","author":"B Pang","year":"2018","unstructured":"Pang B, Shi F-G (2018) Strong inclusion orders between $$L$$-subsets and its applications in $$L$$-convex spaces. Quaest Math 41(8):1021\u20131043","journal-title":"Quaest Math"},{"key":"1690_CR13","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.fss.2018.05.012","volume":"369","author":"B Pang","year":"2019","unstructured":"Pang B, Shi F-G (2019) Fuzzy counterparts of hull operators and interval operators in the framework of $$L$$-convex spaces. Fuzzy Sets Syst 369:20\u201339","journal-title":"Fuzzy Sets Syst"},{"key":"1690_CR14","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.fss.2018.08.002","volume":"369","author":"B Pang","year":"2019","unstructured":"Pang B, Xiu Z-Y (2019) An axiomatic approach to bases and subbases in $$L$$-convex spaces and their applications. Fuzzy Sets Syst 369:40\u201356","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"1690_CR15","first-page":"51","volume":"13","author":"B Pang","year":"2016","unstructured":"Pang B, Zhao Y (2016) Characterization of $$L$$-convex spaces. Iran J Fuzzy Syst 13(4):51\u201361","journal-title":"Iran J Fuzzy Syst"},{"issue":"3","key":"1690_CR16","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1080\/16073606.1997.9632018","volume":"20","author":"SE Rodabaugh","year":"1997","unstructured":"Rodabaugh SE (1997) Powerset operator based foundation for point-set lattice-theoretic (poslat) fuzzy set theories and topologies. Quaest Math 20(3):463\u2013530","journal-title":"Quaest Math"},{"key":"1690_CR17","unstructured":"Rosa MV (1994a) A study of fuzzy convexity with special reference to separation properties. Ph.D. Thesis, Cochin University of Science and Technology, Kerala, India"},{"key":"1690_CR18","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0165-0114(94)90076-0","volume":"62","author":"MV Rosa","year":"1994","unstructured":"Rosa MV (1994b) On fuzzy topology fuzzy convexity spaces and fuzzy local convexity. Fuzzy Sets Syst 62:97\u2013100","journal-title":"Fuzzy Sets Syst"},{"issue":"13","key":"1690_CR19","doi-asserted-by":"publisher","first-page":"4151","DOI":"10.2298\/FIL1913151S","volume":"33","author":"OR Sayed","year":"2019","unstructured":"Sayed OR, El-Sanousy E, Raghp Sayed YH (2019) On $$(L, M)$$-fuzzy convex structures. Filomat 33(13):4151\u20134163","journal-title":"Filomat"},{"issue":"1","key":"1690_CR20","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.fss.2019.02.009","volume":"380","author":"C Shen","year":"2020","unstructured":"Shen C, Shi F-G (2020) Characterizations of $$L$$-convex spaces via domain theory. Fuzzy Sets Syst 380(1):44\u201363","journal-title":"Fuzzy Sets Syst"},{"key":"1690_CR21","doi-asserted-by":"publisher","first-page":"409","DOI":"10.3233\/IFS-151765","volume":"30","author":"F-G Shi","year":"2015","unstructured":"Shi F-G, Li E-Q (2015) The restricted hull operator of $$M$$-fuzzifying convex structures. J Intell Fuzzy Syst 30:409\u2013421","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR22","doi-asserted-by":"publisher","first-page":"3655","DOI":"10.22436\/jnsa.010.07.25","volume":"10","author":"F-G Shi","year":"2017","unstructured":"Shi F-G, Xiu Z-Y (2017) $$(L, M)$$-fuzzy convex structures. J Nonlinear Sci Appl 10:3655\u20133669","journal-title":"J Nonlinear Sci Appl"},{"key":"1690_CR23","first-page":"535","volume":"272","author":"VP Soltan","year":"1983","unstructured":"Soltan VP (1983) d-Convexity in graphs, (Russian). Dokl Akad Nauk SSSR 272:535\u2013537","journal-title":"Dokl Akad Nauk SSSR"},{"key":"1690_CR24","volume-title":"Introduction to the axiomatic theory of convexity, (Russian)","author":"VP Soltan","year":"1984","unstructured":"Soltan VP (1984) Introduction to the axiomatic theory of convexity, (Russian). Shtiinca, Kishinev"},{"key":"1690_CR25","first-page":"89","volume":"11","author":"AP \u0160ostak","year":"1985","unstructured":"\u0160ostak AP (1985) On a fuzzy topological structure Rend. Circ Mat Palermo 11:89\u2013103","journal-title":"Circ Mat Palermo"},{"key":"1690_CR26","series-title":"North-Holland mathematical library","volume-title":"Theory of convex structures","author":"MLJ Van de Vel","year":"1993","unstructured":"Van de Vel MLJ (1993) Theory of convex structures. North-Holland mathematical library. North-Holland Publishing CO., Amsterdam"},{"key":"1690_CR27","series-title":"Mathematical centre tracts","volume-title":"Supercompactness and Wallman spaces","author":"J Van Mill","year":"1977","unstructured":"Van Mill J (1977) Supercompactness and Wallman spaces. Mathematical centre tracts. Mathematisch Centrum, Amsterdam"},{"key":"1690_CR28","first-page":"1143","volume":"23","author":"JC Varlet","year":"1975","unstructured":"Varlet JC (1975) Remarks on distributive lattices. Bull Acad Pol Sci Ser Sci Math Astron Phys 23:1143\u20131147","journal-title":"Bull Acad Pol Sci Ser Sci Math Astron Phys"},{"issue":"3","key":"1690_CR29","doi-asserted-by":"publisher","first-page":"3751","DOI":"10.3233\/JIFS-182963","volume":"37","author":"K Wang","year":"2019","unstructured":"Wang K, Pang B (2019) Coreflectivities of $$(L, M)$$-fuzzy convex structures and $$(L, M)$$-fuzzy cotopologies in $$(L, M)$$-fuzzy closure systems. J Intell Fuzzy Syst 37(3):3751\u20133761","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR30","unstructured":"Wang K, Shi F-G (2018) $$M$$-fuzzifying topological convex spaces. Iran J Fuzzy Syst 15(6):159\u2013174"},{"issue":"1","key":"1690_CR31","first-page":"173","volume":"16","author":"X-Y Wu","year":"2019","unstructured":"Wu X-Y, Li E-Q (2019) Category and subcategories of $$(L, M)$$-fuzzy convex spaces. Iran J Fuzzy Syst 16(1):173\u2013190","journal-title":"Iran J Fuzzy Syst"},{"key":"1690_CR32","doi-asserted-by":"publisher","first-page":"385","DOI":"10.3233\/JIFS-181504","volume":"36","author":"Z-Y Xiu","year":"2019","unstructured":"Xiu Z-Y, Li Q-G (2019a) Relations among $$(L, M)$$-fuzzy convex structures, $$(L, M)$$-fuzzy closure systems and $$(L, M)$$-fuzzy Alexandrov topologies in a degree sense. J Intell Fuzzy Syst 36:385\u2013396","journal-title":"J Intell Fuzzy Syst"},{"issue":"4","key":"1690_CR33","doi-asserted-by":"publisher","first-page":"5719","DOI":"10.3233\/JIFS-181663","volume":"37","author":"Z-Y Xiu","year":"2019","unstructured":"Xiu Z-Y, Li Q-G (2019b) Some characterizations of $$(L, M)$$-fuzzy convex spaces. J Intell Fuzzy Syst 37(4):5719\u20135730","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR34","doi-asserted-by":"publisher","first-page":"613","DOI":"10.3233\/JIFS-16661","volume":"33","author":"Z-Y Xiu","year":"2017","unstructured":"Xiu Z-Y, Pang B (2017) $$M$$-fuzzifying cotopological spaces and $$M$$-fuzzifying convex spaces as $$M$$-fuzzifying closure spaces. J Intell Fuzzy Syst 33:613\u2013620","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"1690_CR35","first-page":"75","volume":"15","author":"Z-Y Xiu","year":"2018","unstructured":"Xiu Z-Y, Pang B (2018) Base axioms and subbase axioms in $$M$$-fuzzifying convex spaces. Iran J Fuzzy Syst 15(2):75\u201387","journal-title":"Iran J Fuzzy Syst"},{"key":"1690_CR36","first-page":"145","volume":"14","author":"Z-Y Xiu","year":"2017","unstructured":"Xiu Z-Y, Shi F-G (2017) $$M$$-fuzzifying interval spaces. Iran J Fuzzy Syst 14:145\u2013162","journal-title":"Iran J Fuzzy Syst"},{"key":"1690_CR37","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"issue":"5","key":"1690_CR38","doi-asserted-by":"publisher","first-page":"8765","DOI":"10.3233\/JIFS-200340","volume":"40","author":"H Zhao","year":"2021","unstructured":"Zhao H, Sayed OR, El-Sanousy E, Ragheb Sayed YH, Chen GX (2021a) On separation axioms in $$(L, M)$$-fuzzy convex structures. J Intell Fuzzy Syst 40(5):8765\u20138773","journal-title":"J Intell Fuzzy Syst"},{"key":"1690_CR39","doi-asserted-by":"crossref","unstructured":"Zhao H, Song Q-L, Sayed OR, El-Sanousy E, Ragheb Sayed YH, Chen G-X (2021b) Corrigendum to \u201cOn $$(L, M)$$-fuzzy convex structures\u201d. Filomat 35(2)","DOI":"10.2298\/FIL2105687Z"},{"issue":"6","key":"1690_CR40","doi-asserted-by":"publisher","first-page":"6619","DOI":"10.3233\/JIFS-18659","volume":"36","author":"Y Zhong","year":"2019","unstructured":"Zhong Y, Shi F-G, Zou J-T, Zou C-Y (2019) Degrees of $$(L, M)$$-fuzzy convexities. J Intell Fuzzy Syst 36(6):6619\u20136629","journal-title":"J Intell Fuzzy Syst"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01690-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01690-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01690-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T13:23:51Z","timestamp":1638537831000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01690-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,12]]},"references-count":40,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["1690"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01690-5","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,12]]},"assertion":[{"value":"15 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"301"}}