{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:39:08Z","timestamp":1777703948201,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T00:00:00Z","timestamp":1566432000000},"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":[[2020,1,9]]},"abstract":"<jats:p>\n                    In this paper, the characterization of\n                    <jats:italic>\u0393<\/jats:italic>\n                    -convergence for the first countable topological spaces, characterization of convergence in supremum metric in general setting and some mutual relation between these convergences are discussed. The\n                    <jats:italic>\u0393<\/jats:italic>\n                    -convergence is defined as the Kuratowaski-Painlev\u00e9 convergence of the endographs of the intuitionistic fuzzy sets. The supremum metric is the supremum of Hausdroff distance among the\n                    <jats:italic>\u03b7<\/jats:italic>\n                    -cuts of the intuitionistic fuzzy sets. To study these convergences is an important part of the theoretical fundamentals for intuitionistic fuzzy set theory. Some results are given as an application to variational analysis.\n                  <\/jats:p>","DOI":"10.3233\/jifs-179429","type":"journal-article","created":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T10:53:48Z","timestamp":1566557628000},"page":"553-564","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Certain convergences for intuitionistic fuzzy sets"],"prefix":"10.1177","volume":"38","author":[{"given":"Zia","family":"Bashir","sequence":"first","affiliation":[{"name":"Quaid-i-Azam University, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tabasam","family":"Rashid","sequence":"additional","affiliation":[{"name":"University of Management and Technology, Lahore, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"Sa\u0142abun","sequence":"additional","affiliation":[{"name":"West Pomeranian University of Technology, Szczecin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohail","family":"Zafar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,8,22]]},"reference":[{"key":"e_1_3_2_2_2","article-title":"Lacunary \u0394-statistical convergence in intuitionistic fuzzy n-normed space","volume":"40","author":"Altunda\u011f S.","year":"2014","unstructured":"Altunda\u011fS. and KamberE., Lacunary \u0394-statistical convergence in intuitionistic fuzzy n-normed space, J Inequal Appl 40 (2014).","journal-title":"J Inequal Appl"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_4_2","doi-asserted-by":"crossref","unstructured":"AtanassovK. Intuitionistic fuzzy sets. Theory and applications Heidelberg: Physica-Verlag (1999).","DOI":"10.1007\/978-3-7908-1870-3_5"},{"key":"e_1_3_2_5_2","doi-asserted-by":"crossref","unstructured":"AtanassovK. On intuitionistic fuzzy sets theory Springer Berlin (2012).","DOI":"10.1007\/978-3-642-29127-2"},{"key":"e_1_3_2_6_2","unstructured":"BanA. Intuitionistic fuzzy measures. Theory and applications Nova Science Publishers New York (2006)."},{"key":"e_1_3_2_7_2","article-title":"Topologies on closed and closed convex sets","author":"Beer G.","year":"1993","unstructured":"BeerG., Topologies on closed and closed convex sets, Mathematics and its Applications, 268, Kluwer Academic Publishers (1993).","journal-title":"Mathematics and its Applications"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.08.018"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-17744"},{"key":"e_1_3_2_10_2","first-page":"205","article-title":"A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces,189\u00e2\u0102\u015e","volume":"442","author":"Bonder J.F.","year":"2016","unstructured":"BonderJ.F., SaintierN., SilvaA., A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces,189\u00e2\u0102\u015e, Journal of Mathematical Analysis and Applications 442 (2016), 205.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"e_1_3_2_11_2","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.ins.2014.06.013","article-title":"Convergences and topology via sequences of multifunctions","volume":"282","author":"Croitoru A.","year":"2014","unstructured":"CroitoruA., Convergences and topology via sequences of multifunctions, Inform Sci 282 (2014), 250\u2013260.","journal-title":"Inform Sci"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.06.001"},{"issue":"6","key":"e_1_3_2_13_2","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1016\/j.na.2005.06.038","article-title":"Supremum metric and relatively compact sets of fuzzy sets","volume":"64","author":"Greco G.H.","year":"2006","unstructured":"GrecoG.H., MoschenM.P., Supremum metric and relatively compact sets of fuzzy sets, Nonlinear Anal-Theor 64(6) (2006), 1325\u20131335.","journal-title":"Nonlinear Anal-Theor"},{"key":"e_1_3_2_14_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02828014","article-title":"Frota Rezende, On the variational convergence of fuzzy sets in metric spaces","volume":"44","author":"Greco G.H.","year":"1998","unstructured":"GrecoG.H., MoschenM.P., QuelhoE., Frota Rezende, On the variational convergence of fuzzy sets in metric spaces, Ann Univ Ferrara, Nuova Ser, Sez VII 44 (1998), 27\u201339.","journal-title":"Ann Univ Ferrara, Nuova Ser, Sez VII"},{"key":"e_1_3_2_15_2","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.fss.2014.05.007","article-title":"std\u2014 Convergence in fuzzy metric spaces","volume":"267","author":"Gregori V.","year":"2015","unstructured":"GregoriV., Mi\u00f1anaJ.J., std\u2014 Convergence in fuzzy metric spaces, Fuzzy Sets Syst 267 (2015), 140\u2013143.","journal-title":"Fuzzy Sets Syst"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.02.044"},{"key":"e_1_3_2_17_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0165-0114(85)90006-5","article-title":"On the convergence of fuzzy sets","volume":"17","author":"Kaleva O.","year":"1985","unstructured":"KalevaO., On the convergence of fuzzy sets, Fuzzy Sets Syst 17 (1985), 53\u201365.","journal-title":"Fuzzy Sets Syst"},{"key":"e_1_3_2_18_2","doi-asserted-by":"crossref","unstructured":"LucchettiR. Convexity and Well-Posed Problems CMS Books Math Springer (2006).","DOI":"10.1007\/0-387-31082-7"},{"issue":"3","key":"e_1_3_2_19_2","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1016\/j.chaos.2009.03.086","article-title":"On generalized statistical convergence in intuitionistic fuzzy normed space","volume":"42","author":"Mohiuddine S.A.","year":"2009","unstructured":"MohiuddineS.A., LohaniQ.M.D., On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos, Solitons Fractals 42(3) (2009), 1731\u20131737.","journal-title":"Chaos, Solitons Fractals"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.07.005"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.11.002"},{"key":"e_1_3_2_22_2","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.fss.2014.03.005","article-title":"Convergence of fuzzy sets with respect to the supremum metric","volume":"245","author":"Pedraza T.","year":"2014","unstructured":"PedrazaT., Rodr\u00edguez-L\u00f3pezJ., RomagueraS., Convergence of fuzzy sets with respect to the supremum metric, Fuzzy Sets Syst 245 (2014), 83\u2013100.","journal-title":"Fuzzy Sets Syst"},{"key":"e_1_3_2_23_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00365-018-9437-3","article-title":"On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence","volume":"48","author":"Berman R.J.","year":"2018","unstructured":"BermanR.J., On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence, Constructive Approximation 48 (2018), 3\u201330.","journal-title":"Constructive Approximation"},{"key":"e_1_3_2_24_2","article-title":"Variational Analysis","author":"Rockafellar R.T.","year":"1998","unstructured":"RockafellarR.T., WetsR.J.-B., Variational Analysis, Comprehensive Studies in Mathematics, 317, Springer, (1998).","journal-title":"Comprehensive Studies in Mathematics"},{"issue":"11","key":"e_1_3_2_25_2","doi-asserted-by":"crossref","first-page":"2978","DOI":"10.1016\/j.mcm.2011.07.020","article-title":"Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces","volume":"54","author":"Sen M.","year":"2011","unstructured":"SenM., DebnathP., Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, Math Comput Model 54(11-12) (2011), 2978\u20132985.","journal-title":"Math Comput Model"},{"issue":"8","key":"e_1_3_2_26_2","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1016\/j.fss.2009.07.005","article-title":"Characterization of the sendographconvergence of fuzzy sets by means of their Lp-and level wise convergence","volume":"161","author":"Trutschnig W.","year":"2010","unstructured":"TrutschnigW., Characterization of the sendographconvergence of fuzzy sets by means of their Lp-and level wise convergence, Fuzzy Sets Syst 161(8) (2010), 1064\u20131077.","journal-title":"Fuzzy Sets Syst"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-179429","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-179429","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-179429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:03Z","timestamp":1777455603000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-179429"}},"subtitle":[],"editor":[{"given":"Cengiz","family":"Kahraman","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,8,22]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1,9]]}},"alternative-id":["10.3233\/JIFS-179429"],"URL":"https:\/\/doi.org\/10.3233\/jifs-179429","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,22]]}}}