{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T18:20:33Z","timestamp":1778696433113,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T00:00:00Z","timestamp":1535846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.<\/jats:p>","DOI":"10.3390\/g9030062","type":"journal-article","created":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T10:50:51Z","timestamp":1535971851000},"page":"62","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Matrix Games with Interval-Valued 2-Tuple Linguistic Information"],"prefix":"10.3390","volume":"9","author":[{"given":"Anjali","family":"Singh","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anjana","family":"Gupta","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,2]]},"reference":[{"key":"ref_1","unstructured":"Neumann, J.V., and Morgenstern, O. 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