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Dual hesitant fuzzy matrix games: based on new similarity measure

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Abstract

The dual hesitant fuzzy set is an effective mathematical approach to deal with the data which are imprecise, uncertain or incomplete information. Dual hesitant fuzzy set is an extension of hesitant fuzzy set which encloses fuzzy set, intuitionistic fuzzy set and hesitant fuzzy set as a special one. In this paper, the axiomatic definition of similarity measure between the dual hesitant fuzzy set is presented. A new similarity measure by considering membership and non-membership functions of dual hesitant fuzzy set is introduced. It is shown that the corresponding distance measure can be obtained from the proposed similarity measure. To check the utility, the proposed similarity measure is applied in a bidirectional approximate reasoning system into matrix game. Matrix game with precise data is hardly applicable in real-life decision-making problem. In view of more realistic sense, we choose the elements as dual hesitant fuzzy into the payoff of the matrix game, which is treated as dual hesitant fuzzy matrix game. Mathematical formulation of dual hesitant fuzzy matrix game with on restriction (DHFMGR) is described. Four algorithms are emerged on the proposed similarity measure, which are provoked to find the optimal value of the DHFMGR. A numerical example is incorporated to illustrate the applicability and feasibility of the proposed measure in dual hesitant fuzzy matrix game. The paper ends with the conclusions including an outlook for future study in this direction.

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Acknowledgements

The author, Jishu Jana, would like to thank to Council of Scientific and Industrial Research (CSIR) for supporting the financial support to continue this research work under JRF scheme with sanctioned Grant No. 09/599(0067)/2016-EMR-I dated 20/10/2016. The research of Sankar Kumar Roy is partially supported by the Portuguese Foundation for Science and Technology (“ FCT-Fundação para a Ciência e a Tecnologia”), through the CIDMA—Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal, within project UID/MAT/04106/2013. The authors are very much thankful to the Managing Editor, Prof. Raffaele Cerulli and anonymous reviewer for their precious comments that help us so much to rigorously improve the quality of the paper.

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Correspondence to Sankar Kumar Roy.

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Jana, J., Roy, S.K. Dual hesitant fuzzy matrix games: based on new similarity measure. Soft Comput 23, 8873–8886 (2019) doi:10.1007/s00500-018-3486-1

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Keywords

  • Matrix games
  • Hesitant fuzzy set
  • Dual hesitant fuzzy set
  • Similarity measure
  • Bidirectional approximate reasoning system