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Matrix Games with Interval-Valued 2-Tuple Linguistic Information

Author

Listed:
  • Anjali Singh

    (Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India)

  • Anjana Gupta

    (Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India)

Abstract

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.

Suggested Citation

  • Anjali Singh & Anjana Gupta, 2018. "Matrix Games with Interval-Valued 2-Tuple Linguistic Information," Games, MDPI, vol. 9(3), pages 1-19, September.
    • Handle: RePEc:gam:jgames:v:9:y:2018:i:3:p:62-:d:167312
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    References listed on IDEAS

    as
    1. Badredine Arfi, 2006. "Linguistic Fuzzy-Logic Game Theory," Journal of Conflict Resolution, Peace Science Society (International), vol. 50(1), pages 28-57, February.
    2. Badredine Arfi, 2006. "Linguistic Fuzzy-Logic Social Game of Cooperation," Rationality and Society, , vol. 18(4), pages 471-537, November.
    3. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    Full references (including those not matched with items on IDEAS)

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