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Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India
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Games 2018, 9(3), 62; https://doi.org/10.3390/g9030062
Received: 11 July 2018 / Revised: 15 August 2018 / Accepted: 29 August 2018 / Published: 2 September 2018
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. View Full-Text
Keywords: 2-tuple linguistic model; interval-valued 2-tuple linguistic model; linguistic linear programming problem; interval-valued linguistic matrix game 2-tuple linguistic model; interval-valued 2-tuple linguistic model; linguistic linear programming problem; interval-valued linguistic matrix game
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Singh, A.; Gupta, A. Matrix Games with Interval-Valued 2-Tuple Linguistic Information. Games 2018, 9, 62.

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