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Linear Programming Technique To Solve Two Person Matrix Games With Interval Pay-Offs

Author

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  • PRASUN KUMAR NAYAK

    (Bankura Christian College, Bankura, 722 101, India)

  • MADHUMANGAL PAL

    (Department of Applied Mathematics with Oceanology, and Computer Programming, Vidyasagar University, Midnapore, 721 102, India)

Abstract

A fuzzy two person interval game problem is proposed and treated in this paper which is not easily tackled by the conventional methods. First, with respect to this pay-off values, a necessary and sufficient condition for the existence of a saddle point is proved. Based on interval value model, we are to find the value of interval game without saddle point. Finally, example is given to illustrate the procedure and to indicate the performance of the proposed method.

Suggested Citation

  • Prasun Kumar Nayak & Madhumangal Pal, 2009. "Linear Programming Technique To Solve Two Person Matrix Games With Interval Pay-Offs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 285-305.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:02:n:s0217595909002201
    DOI: 10.1142/S0217595909002201
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    Citations

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    Cited by:

    1. Deng, Xinyang & Liu, Qi & Deng, Yong, 2016. "Matrix games with payoffs of belief structures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 868-879.
    2. Laxminarayan Sahoo, 2019. "Solving matrix games with linguistic payoffs," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 484-490, August.
    3. Liu, Zhi & Zheng, Xiao-Xue & Li, Deng-Feng & Liao, Chen-Nan & Sheu, Jiuh-Biing, 2021. "A novel cooperative game-based method to coordinate a sustainable supply chain under psychological uncertainty in fairness concerns," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    4. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    5. Ajay Kumar Bhurjee & Geetanjali Panda, 2017. "Optimal strategies for two-person normalized matrix game with variable payoffs," Operational Research, Springer, vol. 17(2), pages 547-562, July.
    6. Sanjiv Kumar & Ritika Chopra & Ratnesh R. Saxena, 2016. "A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-14, December.
    7. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.

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