{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T09:48:29Z","timestamp":1775036909571,"version":"3.50.1"},"reference-count":64,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T00:00:00Z","timestamp":1671753600000},"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":[[2023,3,9]]},"abstract":"<jats:p>Game theory has been successfully applied in a variety of domains to deal with competitive environments between individuals or groups. The matrix games involving fuzzy, interval fuzzy, and intuitionistic fuzzy numbers exclusively examine the numeric components of an issue. However, several researchers have also examined various extensions of conventional game theory, considering the ambiguous situations for payoffs and goals. In many real-life scenarios, qualitative information is often critical in expressing the payoffs of a matrix game. Thus, the present work contributes to the field of matrix games where the payoffs have been quantified via qualitative variables, termed interval-valued hesitant fuzzy linguistic sets. The mathematical formulation and solution concept for matrix games involving interval-valued hesitant fuzzy linguistic numbers is designed by utilizing an aggregation operator supported by linguistic scale function and solving them by employing score function. Finally, the proposed approach is validated by applying it to electric vehicle sales.<\/jats:p>","DOI":"10.3233\/jifs-222466","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T11:49:30Z","timestamp":1671796170000},"page":"5085-5105","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Matrix games involving interval-valued hesitant fuzzy linguistic sets and its application to electric vehicles"],"prefix":"10.1177","volume":"44","author":[{"given":"Deeba R.","family":"Naqvi","sequence":"first","affiliation":[{"name":"Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, India"},{"name":"Department of Applied Sciences, Maharaja Surajmal Institute of Technology, C-4 Janakpuri, New Delhi, India"}]},{"given":"Geeta","family":"Sachdev","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, India"}]},{"given":"Izhar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Fahd University of Petroleum and Minerals, Dahran, Saudi Arabia"},{"name":"Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals, Dahran, Saudi Arabia"}]}],"member":"179","published-online":{"date-parts":[[2022,12,23]]},"reference":[{"issue":"2012","key":"e_1_3_1_2_2","first-page":"401","article-title":"Application ofAtanassov\u2019s I-fuzzy set theory to matrix games withfuzzy goals andfuzzy payoffs","volume":"4","author":"Aggarwal A.","unstructured":"AggarwalA., DubeyD., ChandraS. and MehraA., Application ofAtanassov\u2019s I-fuzzy set theory to matrix games withfuzzy goals andfuzzy payoffs, Fuzzy Information and Engineering 4(2012), 401\u2013414.","journal-title":"Fuzzy Information and Engineering"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9123-z"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2017.08.005"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1177\/0022002705284708"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_1_7_2","first-page":"17","article-title":"Ideas for intuitionistic fuzzy equations, inequalities and optimization","volume":"1","author":"Atanassov K.T.","year":"1995","unstructured":"AtanassovK.T., Ideas for intuitionistic fuzzy equations, inequalities and optimization, Notes on Intuitionistic FuzzySets 1 (1995), 17\u201324.","journal-title":"Notes on Intuitionistic FuzzySets"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/12460125.2013.797320"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.4236\/ojop.2013.21002"},{"key":"e_1_3_1_10_2","unstructured":"BectorC. and ChandraS. Fuzzy mathematical programming and fuzzy matrix games Springer-Verlag 2005."},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:FODM.0000036866.18909.f1"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(03)00260-4"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-019-00191-5"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-019-00638-9"},{"key":"e_1_3_1_15_2","doi-asserted-by":"crossref","unstructured":"BrikaaM. ZhengZ. and AmmarE. Mehar approach for solving matrix games with triangular dual hesitant fuzzy payoffs Granular Computing (2021) pp. 1\u201320.","DOI":"10.1007\/s41066-021-00292-0"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym11050702"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/math8030305"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90260-1"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.04.020"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/593185"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.04.031"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.09.009"},{"key":"e_1_3_1_23_2","unstructured":"DuboisD. and Prade Fuzzy Sets and Systems: Theory and Applications volume 16. Academic Press 1980."},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.03.034"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1958-0"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.890332"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/3477.915345"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-3486-1"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1080\/02522667.2016.1164999"},{"issue":"2010","key":"e_1_3_1_30_2","first-page":"1112","article-title":"Mathematical-programming approach to matrix games with payoffs represented by Atanassov\u2019s interval-valued intuitionistic fuzzy sets","volume":"18","author":"Li D.F.","unstructured":"LiD.F., Mathematical-programming approach to matrix games with payoffs represented by Atanassov\u2019s interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems 18(2010), 1112\u20131128.","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488509006157"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00509-2"},{"key":"e_1_3_1_33_2","doi-asserted-by":"crossref","unstructured":"MartinezL. RuanD. HerreraF. Herrera-ViedmaE. and WangP.P. Linguistic decision making: Tools and Applications 2009.","DOI":"10.1016\/j.ins.2008.12.017"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.05.019"},{"issue":"2010","key":"e_1_3_1_35_2","first-page":"280","article-title":"A lexicographic method for matrixgames with payoffs of triangular intuitionistic fuzzy numbers","volume":"3","author":"Nan J.X.","unstructured":"NanJ.X., LiD.F. and ZhangM.J., A lexicographic method for matrixgames with payoffs of triangular intuitionistic fuzzy numbers, International Journal of Computational Intelligence Systems 3(2010), 280\u2013289.","journal-title":"International Journal of Computational Intelligence Systems"},{"issue":"2014","key":"e_1_3_1_36_2","first-page":"444","article-title":"Intuitionistic fuzzy programming models for matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers","volume":"16","author":"Nan J.X.","unstructured":"NanJ.X., ZhangM.J. and LiD.F., Intuitionistic fuzzy programming models for matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers, International Journal of Fuzzy Systems 16(2014), 444\u2013456.","journal-title":"International Journal of Fuzzy Systems"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-019-00200-7"},{"key":"e_1_3_1_38_2","unstructured":"NeumannV. and MorgensternO. Theory of games and economic behavior. Princeton University Press 1944."},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2012.710442"},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2170076"},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90169-4"},{"issue":"4","key":"e_1_3_1_42_2","first-page":"25","article-title":"Solving matrix games with hesitant fuzzy pay-offs","volume":"17","author":"Seikh M.R.","year":"2020","unstructured":"SeikhM.R., KarmakarS. and XiaM., Solving matrix games with hesitant fuzzy pay-offs, Iranian Journal of Fuzzy Systems 17(4) (2020), 25\u201340.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_43_2","doi-asserted-by":"publisher","DOI":"10.3390\/g9030062"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-018-2810-6"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2017.09.048"},{"issue":"6","key":"e_1_3_1_46_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V.","year":"2010","unstructured":"TorraV., Hesitant fuzzy sets, International Journal ofIntelligent Systems 25(6) (2010), 529\u2013539.","journal-title":"International Journal ofIntelligent Systems"},{"key":"e_1_3_1_47_2","first-page":"1378","article-title":"On hesitant fuzzy sets and decision","volume":"4","author":"Torra V.","year":"2009","unstructured":"TorraV. and NarukawaY., On hesitant fuzzy sets and decision, In The 18th IEEE International Conference on Fuzzy Systems. Jeju Island Korea 4 (2009), 1378\u20131382.","journal-title":"In The 18th IEEE International Conference on Fuzzy Systems. Jeju Island Korea"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-015-0452-4"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-201540"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-021-10014-2"},{"issue":"4","key":"e_1_3_1_51_2","first-page":"149","article-title":"On matrix games with 2-tuple intuitionistic fuzzy linguistic payoffs","volume":"18","author":"Verma R.","year":"2021","unstructured":"VermaR. and AggarwalA., On matrix games with 2-tuple intuitionistic fuzzy linguistic payoffs, Iranian Journal of Fuzzy Systems 18(4) (2021), 149\u2013167.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_52_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-004-4202-4"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2004.07.007"},{"key":"e_1_3_1_54_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-007-9015-9"},{"key":"e_1_3_1_55_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.07.034"},{"key":"e_1_3_1_56_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2017.1413100"},{"key":"e_1_3_1_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.09.002"},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2019.2958635"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-16229"},{"key":"e_1_3_1_60_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2003.10.006"},{"key":"e_1_3_1_61_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-020-01759-4"},{"key":"e_1_3_1_62_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-021-02216-6"},{"issue":"1965","key":"e_1_3_1_63_2","first-page":"338","article-title":"Fuzzy sets","volume":"8","author":"Zadeh L.A.","unstructured":"ZadehL.A., Fuzzy sets, Information and Control 8(1965), 338\u2013353.","journal-title":"Information and Control"},{"key":"e_1_3_1_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_1_65_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90046-8"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-222466","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-222466","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-222466","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T05:52:53Z","timestamp":1769665973000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-222466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,23]]},"references-count":64,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,3,9]]}},"alternative-id":["10.3233\/JIFS-222466"],"URL":"https:\/\/doi.org\/10.3233\/jifs-222466","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,23]]}}}