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Jagdambika Method for Solving Matrix Games with Fuzzy Payoffs

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Recent Developments and the New Direction in Soft-Computing Foundations and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 361))

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Abstract

Li (IEEE Trans Cybern 43:610-621, 2013) [1] recently proposed a method for solving matrix games with fuzzy payoffs and claimed that the obtained minimum expected gain of Player I and maximum expected loss of Player II, will be identical. Chandra and Aggarwal (Eur J Oper Res 2015. https://doi.org/10.1016/j.ejor.2015.05.011) [2], in their recent paper, pointed out the shortcomings of Li’s approach and overcome the shortcomings of Li’s approach. Chandra and Aggarwal, transformed the fuzzy mathematical programming problem into a multiobjective programming problem and obtained its result by using GAMS software. In this paper, it is pointed out that Chandra and Aggarwal have not considered some necessary constraints for the value of game to be a fuzzy number. Further, a new method (named as Jagdambika method) is proposed to overcome the limitations of existing method and to obtain the solution of matrix games with fuzzy payoffs. To illustrate the proposed Jagdambika method, an existing numerical problem of matrix games with fuzzy payoffs is solved by the proposed Jagdambika method.

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References

  1. D.F. Li, An effective methodology for solving matrix games with fuzzy payoffs. IEEE Trans. Cybern. 43, 610–621 (2013)

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Acknowledgements

The authors would like to acknowledge the adolescent inner blessings of Mehar (lovely daughter of Dr. Amit Kumar’s cousin). They believe that Mata Vaishno Devi has appeared on the earth in the form of Mehar and without her blessings it was not possible to think the ideas presented in this paper. The first author also acknowledge the financial support given to her by Department of Science and Technology under INSPIRE Programme for research students [IF130759] to complete Doctoral studies.

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Authors and Affiliations

  1. Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India

    Tina Verma & Amit Kumar

Authors
  1. Tina Verma
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  2. Amit Kumar
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Corresponding author

Correspondence to Tina Verma .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  2. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

  3. Department of Information Technology and Programming, Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

  4. Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Z. Reformat

  5. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

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Verma, T., Kumar, A. (2018). Jagdambika Method for Solving Matrix Games with Fuzzy Payoffs. In: Zadeh, L., Yager, R., Shahbazova, S., Reformat, M., Kreinovich, V. (eds) Recent Developments and the New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-319-75408-6_21

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  • DOI: https://doi.org/10.1007/978-3-319-75408-6_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75407-9

  • Online ISBN: 978-3-319-75408-6

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