{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T19:09:34Z","timestamp":1770750574564,"version":"3.50.0"},"reference-count":11,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,10,5]],"date-time":"2015-10-05T00:00:00Z","timestamp":1444003200000},"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":[[2015,10,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    This paper analyzes the bi-matrix games under the light of birough programming. The combination of bi-matrix games and birough programming produces a new form which is defined here as birough bi-matrix games. In birough bi-matrix games, the payoff elements are characterized by birough variables and uncertainty of the birough variable is measured by birough measure which known as Chance (\n                    <jats:bold>Ch<\/jats:bold>\n                    ). Utilizing the Chance measure, we have defined the expected birough Nash equilibrium strategy for the players which depends upon the confidence level and outcome of the birough bi-matrix game. In order to show the applicability and feasibility of our proposed method, a real-life example on birough bi-matrix game is presented and then solved.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151616","type":"journal-article","created":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T12:05:49Z","timestamp":1444133149000},"page":"863-875","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":17,"title":["Birough programming approach for solving bi-matrix games with birough payoff elements"],"prefix":"10.1177","volume":"29","author":[{"given":"Prasanta","family":"Mula","sequence":"first","affiliation":[{"name":"ISRO Satellite Centre, Old Airport Road, Vimanapura Post, Bangalore, India"}]},{"given":"Sankar Kumar","family":"Roy","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India"}]},{"given":"Deng-Feng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China"}]}],"member":"179","published-online":{"date-parts":[[2015,10,5]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"LiuB2002Theory and Practice of Uncertain ProgrammingPhysica-VerlagHeidelberg"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9145-6"},{"key":"e_1_3_1_4_2","first-page":"71","article-title":"Credibilistic bi-matrix game","volume":"6","author":"Mula P","year":"2012","unstructured":"MulaPRoySK2012Credibilistic bi-matrix gameJournal of Uncertain Systems67180","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_1_5_2","first-page":"10","article-title":"Bifuzzy matrix game","volume":"5","author":"Mula P","year":"2013","unstructured":"MulaPRoySK2013Bifuzzy matrix gameCIIT International Journal of Fuzzy Systems51018","journal-title":"CIIT International Journal of Fuzzy Systems"},{"key":"e_1_3_1_6_2","first-page":"141","article-title":"Fuzzy programming approach to two-person multicriteria bimatrix games","volume":"15","author":"Roy SK","year":"2007","unstructured":"RoySK2007Fuzzy programming approach to two-person multicriteria bimatrix gamesThe Journal of Fuzzy Mathematics15141153","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"e_1_3_1_7_2","unstructured":"RoySK2010Game Theory under MCDM and Fuzzy Set TheoryVDM (Verlag Dr. Muller)Germany"},{"key":"e_1_3_1_8_2","article-title":"Rough set approach to bimatrix game","author":"Roy SK","unstructured":"RoySKMulaPRough set approach to bimatrix gameInternational Journal of Operational ReserachForthcoming (Accepted in 2014)","journal-title":"International Journal of Operational Reserach"},{"key":"e_1_3_1_9_2","first-page":"1","article-title":"Bimatrix game in bifuzzy environment","volume":"1","author":"Roy SK","year":"2014","unstructured":"RoySKMulaP2014Bimatrix game in bifuzzy environmentJournal of Uncertainty Analysis and Applications1117","journal-title":"Journal of Uncertainty Analysis and Applications"},{"key":"e_1_3_1_10_2","first-page":"115","article-title":"A new solution concept in credibilistic game","volume":"3","author":"Roy SK","year":"2011","unstructured":"RoySKMulaPMondalSN2011A new solution concept in credibilistic gameCIIT International Journal of Fuzzy Systems3115120","journal-title":"CIIT International Journal of Fuzzy Systems"},{"key":"e_1_3_1_11_2","unstructured":"BasarTOlsderGJ1995Dynamic Noncooperative Game TheoryLondonAcademic Press"},{"key":"e_1_3_1_12_2","unstructured":"PawlakZ1991Rough Sets: Theoretical Aspects of Reasoning about DataKluwer Academic PublishersDordrecht"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151616","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151616","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151616","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T09:56:07Z","timestamp":1770717367000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151616"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,5]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,10,5]]}},"alternative-id":["10.3233\/IFS-151616"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151616","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,5]]}}}