{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:50Z","timestamp":1760242430395,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T00:00:00Z","timestamp":1502755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach.<\/jats:p>","DOI":"10.3390\/sym9080158","type":"journal-article","created":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T14:35:00Z","timestamp":1502807700000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games"],"prefix":"10.3390","volume":"9","author":[{"given":"Zia","family":"Bashir","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad-45320, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaros\u0142aw","family":"W\u0105tr\u00f3bski","sequence":"additional","affiliation":[{"name":"Department of Web Systems Analysis and Data Processing in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin 71-210, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tabasam","family":"Rashid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore-54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"Sa\u0142abun","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence method and Applied Mathematics in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin 71-210, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jawad","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad-45320, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0165-0114(83)80083-9","article-title":"The use of parametric programming in fuzzy linear programming","volume":"11","author":"Chanas","year":"1983","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0165-0114(87)90105-9","article-title":"An interactive fuzzy programming systems","volume":"23","author":"Werner","year":"1987","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/0377-2217(87)90043-9","article-title":"Interactive multiple object programming subject to flexible constraints","volume":"31","author":"Werner","year":"1987","journal-title":"Eur. 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