{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:52:57Z","timestamp":1777704777657,"version":"3.51.4"},"reference-count":39,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,8,16]],"date-time":"2018-08-16T00:00:00Z","timestamp":1534377600000},"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":[[2019,2,16]]},"abstract":"<jats:p>\n                    In this paper, we will introduce the notions of semiopenness, semicontinuity, preopenness, precontinuity, irresolutness and preirresolutness degree of functions in (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>M<\/jats:italic>\n                    )-fuzzy topological spaces based on the implication operation. Their elementary properties in topology will be extended to the setting of (\n                    <jats:italic>L<\/jats:italic>\n                    ,\n                    <jats:italic>M<\/jats:italic>\n                    )-fuzzy topology through graded concepts. Further we characterize and discuss their relationships with the degree of semi(pre)-compactness, semi(pre)-connectedness,\n                    <jats:bold>Semi -<\/jats:bold>\n                    <jats:italic>T<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    ,\n                    <jats:bold>Pre<\/jats:bold>\n                    -\n                    <jats:italic>T<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    ,\n                    <jats:bold>Semi -<\/jats:bold>\n                    <jats:italic>T<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    , and\n                    <jats:bold>Pre<\/jats:bold>\n                    -\n                    <jats:italic>T<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    .\n                  <\/jats:p>","DOI":"10.3233\/jifs-18251","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T11:23:35Z","timestamp":1534505015000},"page":"787-803","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["New degrees for functions in (\n                    <i>L<\/i>\n                    ,\n                    <i>M<\/i>\n                    )-fuzzy topological spaces based on (\n                    <i>L<\/i>\n                    ,\n                    <i>M<\/i>\n                    )-fuzzy semiopen and (\n                    <i>L<\/i>\n                    ,\n                    <i>M<\/i>\n                    )-fuzzy preopen operators"],"prefix":"10.1177","volume":"36","author":[{"given":"A.","family":"Ghareeb","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt"},{"name":"Department of Mathematics, College of Science, Al-Baha University, Al-Baha, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wadei F.","family":"Al-Omeri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Balqa Applied University, Salt, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,8,16]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(81)90222-5"},{"key":"e_1_3_2_3_2","first-page":"145","article-title":"On fuzzy S-closed spaces","volume":"11","author":"\u00c7oker D.","year":"1987","unstructured":"\u00c7okerD. and \u0118sA.H., On fuzzy S-closed spaces, Doga Tr J Math 11 (1987), 145\u2013152.","journal-title":"Doga Tr J Math"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(68)90057-7"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.06.016"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.5391\/IJFIS.2011.11.1.054"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0642-2"},{"key":"e_1_3_2_8_2","doi-asserted-by":"crossref","unstructured":"GhareebA. and ShiF.-G. SP-compactness and SP-connectedness degree in L-fuzzy pretopological spaces 31 (2016) 1435\u20131445.","DOI":"10.3233\/IFS-162210"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90288-6"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(82)90030-6"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5079-2_5"},{"key":"e_1_3_2_12_2","first-page":"1679","volume":"31","author":"Jin Q.","year":"2016","unstructured":"JinQ., LiL. One-axiom characterizations on lattice-valued closure (interior) operators 31 (2016) 1679\u20131688. 3.","journal-title":"One-axiom characterizations on lattice-valued closure (interior) operators"},{"key":"e_1_3_2_13_2","volume-title":"On fuzzy topologies","author":"Kubiak T.","year":"1985","unstructured":"KubiakT. On fuzzy topologies, Ph.D. Thesis, Adam Mick-iewicz, Poznan, Poland, 1985."},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.4995\/agt.2004.1965"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141238"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-016-9490-x"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90151-F"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-131038"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1720293P"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.2989\/16073606.2017.1308976"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1953-0058568-4"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5079-2_6"},{"key":"e_1_3_2_23_2","article-title":"L-fuzzy semiopenness and L-fuzzy preopenness","author":"Shi F.-G.","unstructured":"ShiF.-G., L-fuzzy semiopenness and L-fuzzy preopenness, J Nonlinear Sci Appl, In Press.","journal-title":"J Nonlinear Sci Appl"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.02.006"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.09.002"},{"key":"e_1_3_2_26_2","doi-asserted-by":"crossref","unstructured":"ShiY. and ShiF.-G. Characterizations of L-topologies 34 (2018) 1 613\u2013623.","DOI":"10.3233\/JIFS-17845"},{"key":"e_1_3_2_27_2","first-page":"89","article-title":"On a fuzzy topological structure","volume":"11","author":"\u0160ostak A.P.","year":"1985","unstructured":"\u0160ostak, A.P., On a fuzzy topological structure, Rendiconti Circolo Matematico Palermo 11(Suppl. Ser. II) (1985), 89\u2013103.","journal-title":"Rendiconti Circolo Matematico Palermo"},{"key":"e_1_3_2_28_2","unstructured":"\u0160ostak A.P. On compactness and connectedness degrees of fuzzy sets in fuzzy topological spaces 1988 Heldermann Verlag Berlin."},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1070\/RM1989v044n06ABEH002295"},{"key":"e_1_3_2_30_2","first-page":"85","article-title":"Towards the concept of a fuzzy category","volume":"562","author":"\u0160ostak A.P.","year":"1991","unstructured":"\u0160ostak, A.P., Towards the concept of a fuzzy category, Acta Univ Latv (Ser Math) 562 (1991), 85\u201394.","journal-title":"Acta Univ Latv (Ser Math)"},{"key":"e_1_3_2_31_2","first-page":"159","article-title":"Fuzzy categories related to algebra and topology","volume":"16","author":"\u0160ostak A.P.","year":"1999","unstructured":"\u0160ostak, A.P., Fuzzy categories related to algebra and topology, Tatra Mount Math Publ 16 (1999), 159\u2013185.","journal-title":"Tatra Mount Math Publ"},{"key":"e_1_3_2_32_2","doi-asserted-by":"crossref","unstructured":"\u0160ostak A.P. L-valued categories: Generalities and examples related to algebra and topology World Scientific publ. (2004) pp291\u2013311.","DOI":"10.1142\/9789812702418_0022"},{"key":"e_1_3_2_33_2","doi-asserted-by":"crossref","unstructured":"XiuZ.-Y. and PangB. M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces 33 (2017) 613\u2013620.","DOI":"10.3233\/JIFS-16661"},{"issue":"2","key":"e_1_3_2_34_2","first-page":"75","article-title":"Base axioms and subbase axioms in M-fuzzifying convex spaces","volume":"15","author":"Xiu Z.-Y.","year":"2018","unstructured":"XiuZ.-Y. and PangB., Base axioms and subbase axioms in M-fuzzifying convex spaces, Iranian Journal of Fuzzy Systems 15(2) (2018), 75\u201387.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.03.003"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.11.010"},{"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":"crossref","unstructured":"ZhanJ. and AlcantudJ.C.R. A survey of parameter reduction of soft sets and corresponding algorithms Artificial Intelligence Review (2017)","DOI":"10.1007\/s10462-017-9592-0"},{"key":"e_1_3_2_39_2","doi-asserted-by":"crossref","unstructured":"ZhanJ. and AlcantudJ.C.R. A novel type of soft rough covering and its application to multicriteria group decision making Artificial Intelligence Review (2018).","DOI":"10.1007\/s10462-018-9617-3"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(85)90025-8"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18251","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18251","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18251","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:59Z","timestamp":1777455719000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,16]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2,16]]}},"alternative-id":["10.3233\/JIFS-18251"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18251","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,16]]}}}