{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:04:03Z","timestamp":1774627443420,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T00:00:00Z","timestamp":1500940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Natural Science Foundations of China","award":["11671001"],"award-info":[{"award-number":["11671001"]}]},{"name":"The National Natural Science Foundations of China","award":["61472056"],"award-info":[{"award-number":["61472056"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we put forward the multi-objective matrix game model based on fuzzy payoffs. In order to solve the game model, we first discuss the relationship of two fuzzy numbers via the lower limit    -  1 2      of the possibility degree. Then, utilizing this relationship, we conclude that the equilibrium solution of this game model and the optimal solution of multicriteria linear optimization problems are of equal value. Finally, to illustrate the effectiveness and correctness of the obtained model, an example is provided.<\/jats:p>","DOI":"10.3390\/sym9080130","type":"journal-article","created":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T10:04:36Z","timestamp":1500977076000},"page":"130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Solving Multi-Objective Matrix Games with Fuzzy Payoffs through the Lower Limit of the Possibility Degree"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4088-5371","authenticated-orcid":false,"given":"Dong","family":"Qiu","sequence":"first","affiliation":[{"name":"College of Science, Chongqing University of Post and Telecommunication, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yumei","family":"Xing","sequence":"additional","affiliation":[{"name":"College of Science, Chongqing University of Post and Telecommunication, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuqiao","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Science, Chongqing University of Post and Telecommunication, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2140\/pjm.1956.6.1","article-title":"An analog of the minimax theorem for vector payoffs","volume":"6","author":"Blackwell","year":"1956","journal-title":"Pac. 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