IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v246y2015i2p575-581.html
   My bibliography  Save this article

On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations

Author

Listed:
  • Chandra, S.
  • Aggarwal, A.

Abstract

The purpose of this paper is to highlight a serious omission in the recent work of Li (2012) for solving the two person zero-sum matrix games with pay-offs of triangular fuzzy numbers (TFNs) and propose a new methodology for solving such games. Li (2012) proposed a method which always assures that the max player gain-floor and min player loss-ceiling have a common TFN value. The present paper exhibits a flaw in this claim of Li (2012). The flaw arises on account of Li (2012) not explaining the meaning of solution of game under consideration. The present paper attempts to provide certain appropriate modifications in Li’s model to take care of this serious omission. These modifications in conjunction with the results of Clemente, Fernandez, and Puerto (2011) lead to an algorithm to solve matrix games with pay-offs of general piecewise linear fuzzy numbers.

Suggested Citation

  • Chandra, S. & Aggarwal, A., 2015. "On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations," European Journal of Operational Research, Elsevier, vol. 246(2), pages 575-581.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:2:p:575-581
    DOI: 10.1016/j.ejor.2015.05.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715003835
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.05.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    3. Deng-Feng Li, 2011. "Notes On "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. 28(06), pages 705-737.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Wen Li & Deyi Li & Yuqiang Feng & Du Zou, 2023. "Fuzzy Weighted Pareto–Nash Equilibria of Multi-Objective Bi-Matrix Games with Fuzzy Payoffs and Their Applications," Mathematics, MDPI, vol. 11(20), pages 1-18, October.
    3. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    4. Zhiying Wang & Xiaodi Liu & Shitao Zhang, 2019. "A New Decision Method for Public Opinion Crisis with the Intervention of Risk Perception of the Public," Complexity, Hindawi, vol. 2019, pages 1-14, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shuying Li & Guoping Tu, 2022. "Probabilistic Linguistic Matrix Game Based on Fuzzy Envelope and Prospect Theory with Its Application," Mathematics, MDPI, vol. 10(7), pages 1-30, March.
    2. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    3. 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.
    4. 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.
    5. Chunguang Bai & Joseph Sarkis, 2013. "Green information technology strategic justification and evaluation," Information Systems Frontiers, Springer, vol. 15(5), pages 831-847, November.
    6. Anjali Singh & Anjana Gupta, 2018. "Matrix Games with Interval-Valued 2-Tuple Linguistic Information," Games, MDPI, vol. 9(3), pages 1-19, September.
    7. Ajay Kumar Bhurjee, 2016. "Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-13, March.
    8. Gaurav Sharma & Sapan Kumar Das & Ganesh Kumar, 2023. "Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1456-1487, September.
    9. Jiacai Liu & Wenjian Zhao, 2016. "Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games," IJERPH, MDPI, vol. 13(11), pages 1-12, November.
    10. Kusi-Sarpong, Simonov & Bai, Chunguang & Sarkis, Joseph & Wang, Xuping, 2015. "Green supply chain practices evaluation in the mining industry using a joint rough sets and fuzzy TOPSIS methodology," Resources Policy, Elsevier, vol. 46(P1), pages 86-100.
    11. M. G. Brikaa & Zhoushun Zheng & El-Saeed Ammar, 2020. "Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals," Mathematics, MDPI, vol. 8(3), pages 1-30, February.
    12. Wen Li & Deyi Li & Yuqiang Feng & Du Zou, 2023. "Fuzzy Weighted Pareto–Nash Equilibria of Multi-Objective Bi-Matrix Games with Fuzzy Payoffs and Their Applications," Mathematics, MDPI, vol. 11(20), pages 1-18, October.
    13. 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.
    14. Vikas Vikram Singh & Abdel Lisser, 2018. "A Characterization of Nash Equilibrium for the Games with Random Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 998-1013, September.
    15. Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    16. Yu, Yanan & He, Yong & Zhao, Xuan, 2021. "Impact of demand information sharing on organic farming adoption: An evolutionary game approach," Technological Forecasting and Social Change, Elsevier, vol. 172(C).
    17. Chen, Yi & Ding, Shuai & Zheng, Handong & Zhang, Youtao & Yang, Shanlin, 2018. "Exploring diffusion strategies for mHealth promotion using evolutionary game model," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 148-161.
    18. 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).
    19. Deng-Feng Li & Yin-Fang Ye, 2018. "Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method," Operational Research, Springer, vol. 18(1), pages 205-220, April.
    20. Chou, Jui-Sheng & Truong, Ngoc-Son, 2019. "Cloud forecasting system for monitoring and alerting of energy use by home appliances," Applied Energy, Elsevier, vol. 249(C), pages 166-177.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:246:y:2015:i:2:p:575-581. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.