Parametric Similarity Measures on Linguistic Single-Valued Neutrosophic Sets with Application to Decision-Making Problems

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 940)


Linguistic single-valued neutrosophic (LSVN) set (LSVNS) is one of the influential contrivance for addressing the decision-making (DM) problems with uncertain and qualitative information by means of degree of acceptance, indeterminacy and non-acceptance in linguistic terms. In DM problems, similarity measure is the basic tool for recognizing associations within or across the given choices. Thus, this paper aims to construct the parametric similarity measure and weighted parametric similarity measure by making use of LSVNSs. The basic axioms of these measures are also highlighted. Further, the manuscript offers the multi-criteria DM approach based on the proposed measures and describes it by a numerical example. Finally, the efficiency and its preferences over the existing methods are confirmed by means of sensitivity and comparative investigation.


Single-valued neutrosophic set Linguistic single-valued neutrosophic set Similarity measure Multi-criteria decision-making 



The author would like to thank the University Grant Commission, New Delhi, India for providing financial support under Maulana Azad National Fellowship scheme wide File No. F1-17.1/2017-18/MANF-2017-18-PUN-82613/(SA-III/Website) during the preparation of this manuscript.


  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Smarandache, F.: A Unifying Field in Logics: Neutrosophic Logic. Philosophy, pp. 1–141 (1999)Google Scholar
  4. 4.
    Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R.: Single valued neutrosophic sets. Rev Air Force Acad 4, 410–413 (2010)zbMATHGoogle Scholar
  5. 5.
    Nancy, G.H.: An improved score function for ranking neutrosophic sets and its application to decision-making process. Int. J. Uncertainty Quantification 6(5), 377–385 (2016)CrossRefGoogle Scholar
  6. 6.
    Nancy, G.H.: Novel single-valued neutrosophic aggregated operators under frank norm operation and its application to decision-making process. Int. J. Uncertainty Quantification 6(4), 361–375 (2016)CrossRefGoogle Scholar
  7. 7.
    Ye, J.: Projection and bidirectional projection measures of single-valued neutrosophic sets and their decision-making method for mechanical design schemes. J. ExpErimEntal thEorEtical artificial intElligEncE 29(4), 731–740 (2017)CrossRefGoogle Scholar
  8. 8.
    Ye, J.: Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput. 21(3), 817–825 (2017)CrossRefGoogle Scholar
  9. 9.
    Garg, H., Nancy: Some new biparametric distance measures on single-valued neutrosophic sets with applications to pattern recognition and medical diagnosis. Information 8(4), 162–181 (2017). Scholar
  10. 10.
    Ji, P., Wang, J.Q., Zhang, H.Y.: Frank prioritized bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers. Neural Comput. Appl. 30(3), 799–823 (2018)CrossRefGoogle Scholar
  11. 11.
    Garg, H., Nancy: Multi-criteria decision-making method based on prioritized muirhead mean aggregation operator under neutrosophic set environment. Symmetry 10(7), 280–304 (2018)CrossRefGoogle Scholar
  12. 12.
    Ye, J.: Multiple-attribute decision-making method using similarity measures of single-valued neutrosophic hesitant fuzzy sets based on least common multiple cardinality. J. Intell. Fuzzy Syst. 34(6), 4203–4211 (2018)CrossRefGoogle Scholar
  13. 13.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—i. Inf. Sci. 8(3), 199–249 (1975)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li, Y.Y., Zhang, H., Wang, J.Q.: Linguistic neutrosophic sets and their application in multicriteria decision-making problems. Int. J. Uncertainty Quantification 7(2), 135–154 (2017)CrossRefGoogle Scholar
  15. 15.
    Fang, Z., Ye, J.: Multiple attribute group decision-making method based on linguistic neutrosophic numbers. Symmetry 9(7), 111–122 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Garg, H., Nancy: Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. J. Ambient Intell. Humanized Comput. 9(6), 1975–1997 (2018). Scholar
  17. 17.
    Fan, C., Ye, J., Hu, K., Fan, E.: Bonferroni mean operators of linguistic neutrosophic numbers and their multiple attribute group decision-making methods. Information 8(3), 107–117 (2017)CrossRefGoogle Scholar
  18. 18.
    Liu, P., You, X.: Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making. PloS ONE 13(3), e0193027 (2018). Scholar
  19. 19.
    Wang, Y., Liu, P.: Linguistic neutrosophic generalized partitioned bonferroni mean operators and their application to multi-attribute group decision making. Symmetry 10(5), 160–194 (2018)CrossRefGoogle Scholar
  20. 20.
    Liang, W., Zhao, G., Wu, H.: Evaluating investment risks of metallic mines using an extended topsis method with linguistic neutrosophic numbers. Symmetry 9(8), 149–166 (2017)CrossRefGoogle Scholar
  21. 21.
    Shi, L., Ye, J.: Multiple attribute group decision-making method using correlation coefficients between linguistic neutrosophic numbers. J. Intell. Fuzzy Syst. 35(1), 917–925 (2018)CrossRefGoogle Scholar
  22. 22.
    Li, Y.Y., Wang, J.Q., Wang, T.L.: A linguistic neutrosophic multi-criteria group decision-making approach with EDAS method. Arab. J. Sci. Eng., 1–13 (2018)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Engineering and Technology (Deemed University)PatialaIndia

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