{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:31:11Z","timestamp":1777703471179,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,4,19]],"date-time":"2018-04-19T00:00:00Z","timestamp":1524096000000},"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":[[2018,4,19]]},"abstract":"<jats:p>\n                    In this paper we establish various gap functions of random mixed variational inequalities in fuzzy environment and then by using the resolvent operator technique, error bounds and global error bounds are derived in terms of regularized and\n                    <jats:italic>D<\/jats:italic>\n                    -gap functions. Finally, we obtain error bounds for random mixed variational inequalities without using Lipschitz continuity assumption. Our work generalizes the previously known results for random variational inequalities.\n                  <\/jats:p>","DOI":"10.3233\/jifs-171370","type":"journal-article","created":{"date-parts":[[2018,4,20]],"date-time":"2018-04-20T11:05:07Z","timestamp":1524222307000},"page":"2313-2324","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Mixed variational inequalities with various error bounds for random fuzzy mappings"],"prefix":"10.1177","volume":"34","author":[{"given":"Suhel Ahmad","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, BITS-Pilani, Dubai Campus, Dubai, UAE"}]},{"given":"Watcharaporn","family":"Cholamjiak","sequence":"additional","affiliation":[{"name":"School of Science, University of Phayao, Phayao, Thailand"}]}],"member":"179","published-online":{"date-parts":[[2018,4,19]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.08.025"},{"key":"e_1_3_1_3_2","first-page":"11","author":"Antipin A.S.","year":"1997","unstructured":"AntipinA.S., Iterative gradient predictor type methods for computing fixed point of external mappings, In: GuddatJ., JondenH.Th., NizickaF., StillG. and TwittF., (eds.) Parametric optimization and related topics IV[C]. Peter Lang, Frankfurt, Main, 1997, pp. 11\u201324.","journal-title":"Parametric optimization and related topics IV[C]"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9801-y"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9898-z"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.03.049"},{"key":"e_1_3_1_7_2","unstructured":"BrezisH. Operateurs Maximaux Monotones et Semigroups de Contractzons dans les Espaces de Hzlbert Amsterdam North-Holland 1973."},{"key":"e_1_3_1_8_2","volume-title":"Fixed Point Theory with Applications","author":"Chang S.S.","year":"1984","unstructured":"ChangS.S., Fixed Point Theory with Applications, Chongqing Publishing House, Chongqing, 1984."},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90178-3"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90135-5"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90268-6"},{"key":"e_1_3_1_12_2","first-page":"497","article-title":"Regularized gap functions and error bounds for vector variational inequality","volume":"6","author":"Charitha C.","year":"2010","unstructured":"CharithaC. and DuttaJ., Regularized gap functions and error bounds for vector variational inequality, Pac J Optim 6 (2010), 497\u2013510.","journal-title":"Pac J Optim"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.03.049"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585696"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0289-4_11"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-011-9733-y"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00222-4"},{"key":"e_1_3_1_18_2","first-page":"89","article-title":"Random generalized set-valued implicit variational inequalities","volume":"18","author":"Huang N.J.","year":"1995","unstructured":"HuangN.J., Random generalized set-valued implicit variational inequalities, J Liaoning Normal Univ 18 (1995), 89\u201393.","journal-title":"J Liaoning Normal Univ"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-007-9248-8"},{"key":"e_1_3_1_20_2","first-page":"35","article-title":"Some results on random generalized games and random quasi-variational inequalities","volume":"2","author":"Husain T.","year":"1994","unstructured":"HusainT., TarafdarE. and YuanX.Z., Some results on random generalized games and random quasi-variational inequalities, Far East J Math Sci 2 (1994), 35\u201355.","journal-title":"Far East J Math Sci"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.03.055"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.03.056"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-015-0945-4"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-016-0984-5"},{"key":"e_1_3_1_25_2","first-page":"53","article-title":"Some recent advances in variational inequalities, Part I, Basic concepts","volume":"26","author":"Noor M.A.","year":"1997","unstructured":"NoorM.A., Some recent advances in variational inequalities, Part I, Basic concepts, New Zealand J Math 26 (1997), 53\u201380.","journal-title":"New Zealand J Math"},{"key":"e_1_3_1_26_2","first-page":"229","article-title":"Some recent advances in variational inequalities, Part II, Other concepts","volume":"26","author":"Noor M.A.","year":"1997","unstructured":"NoorM.A., Some recent advances in variational inequalities, Part II, Other concepts, New Zealand J Math 26 (1997), 229\u2013255.","journal-title":"New Zealand J Math"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.7533"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.011"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.7153\/jmi-01-23"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90257-I"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00323-5"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00131-6"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026506516738"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00554-1"},{"key":"e_1_3_1_35_2","first-page":"55","article-title":"Random variational inequalities and applications to random minimization and nonlinear boundary problems","volume":"4","author":"Tan K.K.","year":"1994","unstructured":"TanK.K., TarafdarE. and YuanX.Z., Random variational inequalities and applications to random minimization and nonlinear boundary problems, Panamer Math J 4 (1994), 55\u201371.","journal-title":"Panamer Math J"},{"key":"e_1_3_1_36_2","first-page":"1267","article-title":"Gap functions and global error bounds for set-valued mixed variational inequalities","volume":"17","author":"Tang G.J.","year":"2013","unstructured":"TangG.J. and HuangN.J., Gap functions and global error bounds for set-valued mixed variational inequalities, Taiwanese J Math 17 (2013), 1267\u20131286.","journal-title":"Taiwanese J Math"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012994277645"},{"key":"e_1_3_1_38_2","first-page":"467","article-title":"Non-compact random generalized games and random quasi-variational inequalities","volume":"7","author":"Yuan X.Z.","year":"1994","unstructured":"YuanX.Z., Non-compact random generalized games and random quasi-variational inequalities, J Appl Stochastic Anal 7 (1994), 467\u2013486.","journal-title":"J Appl Stochastic Anal"},{"key":"e_1_3_1_39_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-171370","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-171370","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171370","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:46Z","timestamp":1777455526000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-171370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,19]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,4,19]]}},"alternative-id":["10.3233\/JIFS-171370"],"URL":"https:\/\/doi.org\/10.3233\/jifs-171370","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,19]]}}}