IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v479y2024ics0096300324003357.html

Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers

Author

Listed:
  • İzgi, Burhaneddin
  • Kocken, Hale Gonce
  • Özkaya, Murat

Abstract

In this paper, we mainly consider the solution of two-person zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers. Contrary to the literature, we focus on developing the methods to solve the game directly based on only the norms of the payoff matrix holistically, without solving a linear programming problem or handling sub-games created by taking the components of fuzzy numbers separately. For this purpose, we first present fuzzy versions of 1-norm and ∞-norm with the help of a ranking function and develop the fuzzy matrix norm method to obtain an approximate solution of the zero-sum fuzzy matrix game. In addition to this approach, we provide the fuzzy extended matrix norm method as an enhanced version of the method, which involves the use of newly defined fuzzy matrix norms. Thus, we managed to avoid the complexity of the optimization process of the linear programming problem via the proposed matrix norm-based methods. Finally, we illustrate the implementation of the methods by considering several benchmark examples and a 3 × 3 fuzzy matrix game.

Suggested Citation

  • İzgi, Burhaneddin & Kocken, Hale Gonce & Özkaya, Murat, 2024. "Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003357
    DOI: 10.1016/j.amc.2024.128874
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324003357
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128874?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

    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. Sumaila, Ussif Rashid, 1999. "A review of game-theoretic models of fishing," Marine Policy, Elsevier, vol. 23(1), pages 1-10, January.
    3. O. G. Haywood, 1954. "Military Decision and Game Theory," Operations Research, INFORMS, vol. 2(4), pages 365-385, November.
    4. repec:cup:astinb:v:21:y:1991:i:01:p:17-40_00 is not listed on IDEAS
    5. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2023. "Extended matrix norm method: Applications to bimatrix games and convergence results," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    6. Liu, Yuyuan & Liu, Linjie & Guo, Ruqiang & Zhang, Liang, 2023. "N-player repeated evolutionary trust game under government management," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. 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.
    8. Benjamin H. Steven, 1961. "An Application Of Game Theory To A Problem In Location Strategy," Papers in Regional Science, Wiley Blackwell, vol. 7(1), pages 143-157, January.
    9. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2024. "Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    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. Siddharth Prajapati & Ramesh Anbanandam, 2026. "Social Sustainability Index for Performance Measurement in Humanitarian Supply Chains: A Novel Fuzzy Logic and TISM–MICMAC Approach," Global Journal of Flexible Systems Management, Springer;Global Institute of Flexible Systems Management, vol. 27(1), pages 17-45, March.

    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. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2024. "Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    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. 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.
    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. Hutton, Trevor & Sumaila, Ussif Rashid, 2002. "Natural Resource Accounting And South African Fisheries: A Bio-Economic Assessment Of The West Coast Deep-Sea Hake Fishery With Reference To The Optimal Utilisation And Management Of The Resource," Discussion Papers 18018, University of Pretoria, Center for Environmental Economics and Policy in Africa.
    6. David M Frank & Sahotra Sarkar, 2010. "Group Decisions in Biodiversity Conservation: Implications from Game Theory," PLOS ONE, Public Library of Science, vol. 5(5), pages 1-10, May.
    7. Chunguang Bai & Joseph Sarkis, 2013. "Green information technology strategic justification and evaluation," Information Systems Frontiers, Springer, vol. 15(5), pages 831-847, November.
    8. Kose, Erkan & Erbas, Mehmet & Ersen, Erkan, 2017. "An integrated approach based on game theory and geographical information systems to solve decision problems," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 105-114.
    9. Bertrand Crettez & Régis Deloche & Ronan Tallec, 2023. "An analytical narrative of the Day of Dupes," Rationality and Society, , vol. 35(4), pages 480-501, November.
    10. Guo, Ruqiang & Liu, Linjie & Liu, Yuyuan & Zhang, Liang, 2024. "Evolution of trust in the N-player trust game with the margin system," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    11. Su, Xin & Guo, Ruqiang & Hua, Shijia & Liu, Linjie & Zhang, Liang, 2025. "Time delay effects on evolutionary dynamics of N-player trust game with diverse investment behaviors," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    12. İzgi, Burhaneddin & Özkaya, Murat & Kemal Üre, Nazım & Perc, Matjaž, 2025. "A holistic matrix norm-based alternative solution method for Markov reward games," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    13. Gakushi Ishimura & Sam Herrick & Ussif Sumaila, 2013. "Fishing games under climate variability: transboundary management of Pacific sardine in the California Current System," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(2), pages 189-209, April.
    14. 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.
    15. Zhu, Enqiang & Chen, Jia & Liu, Shiqi & Zhang, Xiaokai & Liu, Chanjuan, 2025. "The influence of heterogeneous investment on the evolution of trust in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 677(C).
    16. Philippe Mongin, 2018. "A game-theoretic analysis of the Waterloo campaign and some comments on the analytic narrative project," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 12(3), pages 451-480, September.
    17. Dhruva Kartik & Ashutosh Nayyar, 2021. "Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 11(2), pages 363-388, June.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:apmaco:v:479:y:2024:i:c:s0096300324003357. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.