Skip to main content
SpringerLink
Log in

Dual hesitant fuzzy matrix games: based on new similarity measure

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MathSciNet  MATH  Google Scholar 

  • Bector CR, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Springer, Berlin

    MATH  Google Scholar 

  • Bhaumik A, Roy SK, Li DF (2017) Analysis of triangular intuitionistic fuzzy matrix games using robust ranking. J Intell Fuzzy Syst 33(1):327–336

    Article  MATH  Google Scholar 

  • Campos L (1989) Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets Syst 32(3):275–289

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision making problems based on vague sets. Fuzzy Sets Syst 67(2):163–172

    Article  MATH  Google Scholar 

  • Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353

    Article  MathSciNet  MATH  Google Scholar 

  • Hung WL, Yang MS (2007) Similarity measures of intuitionistic fuzzy sets based on \(L_p\) metric. Int J Approx Reason 46(1):120–136

    Article  MATH  MathSciNet  Google Scholar 

  • Li YH, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28(2):278–285

    Article  Google Scholar 

  • Liang ZZ, Shi PF (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24(15):2687–2693

    Article  MATH  Google Scholar 

  • Mula P, Roy SK, Li DF (2015) Birough programming approach for solving bi-matrix games with birough payoff elements. J Intell Fuzzy Syst 29(2):863–875

    Article  MathSciNet  MATH  Google Scholar 

  • Neumann J, Morgenstern O (1944) Theory of games and economic behaviour. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Ning Y, Chen X, Wang Z, Li X (2017) An uncertain multi-objective programming model for machine scheduling problem. Int J Mach Learn Cybern 8(5):1493–1500

    Article  Google Scholar 

  • Owen G (1982) Game theory. Academic press, New York

    MATH  Google Scholar 

  • Roy SK (2007) Fuzzy programming approach to two-person multicriteria bimatrix games. J Fuzzy Math 15(1):141–153

    MathSciNet  MATH  Google Scholar 

  • Roy SK (2010) Game theory under MCDM and fuzzy set theory. VDM (Verlag Dr.Muller), Germany

  • Roy SK, Bhaumik A (2018) Intelligent water management: a triangular type-2 intuitionistic fuzzy matrix games approach. Water Resour Manag 32(3):949–968

    Article  Google Scholar 

  • Roy SK, Mondal SN (2016) An approach to solve fuzzy interval valued matrix game. Int J Oper Res 26(3):253–267

    MathSciNet  MATH  Google Scholar 

  • Roy SK, Mula P (2013) Bimatrix game in bifuzzy rough environment. J Uncertain Anal Appl 1:11. https://doi.org/10.1186/2195-5468-1-11

    Article  Google Scholar 

  • Roy SK, Mula P (2015) Rough set approach to bimatrix game. Int J Oper Res 23(2):229–244

    Article  MathSciNet  MATH  Google Scholar 

  • Roy SK, Mula P (2016) Solving matrix game with rough payoffs using genetic algorithm. Oper Res Int J 16(1):117–130

    Article  Google Scholar 

  • Roy SK, Mula P, Mondal SN (2011) A new solution concept in credibilistic game. CIIT Int J Fuzzy Syst 3(3):115–120

    Google Scholar 

  • Singh P (2014) A new method for solving dual hesitant fuzzy assignment problems with restriction based on similarity measure. Appl Soft Comput 24:559–571

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distance between intutionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518

    Article  MATH  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy syst, Jeju Island, Korea, pp 1378–1382

  • Wu D, Mendel JM (2009) A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf Sci 179(8):1169–1192

    Article  MathSciNet  Google Scholar 

  • Xu FS (2009) A new method on measures of similarity between vague sets. World Congress Comput Sci Inf Eng 4:297–300

    Google Scholar 

  • Xu Z (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180(1):181–190

    Article  MATH  Google Scholar 

  • Xu Z, Xia M (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(1):2128–2138

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–356

    Article  MATH  Google Scholar 

  • Zhu B, Xu Z, Xia M (2012) Dual hesitant fuzzy sets. J Appl Math. https://doi.org/10.1155/2012/879629

    Article  MathSciNet  MATH  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Jishu Jana & Sankar Kumar Roy

Authors
  1. Jishu Jana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sankar Kumar Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sankar Kumar Roy.

Ethics declarations

Conflict of interest

The authors do not have any possible conflicts of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3486-1

Keywords

Search

Navigation