Similarity Measure of Intuitionistic Fuzzy Numbers by the Centroid Point

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 91)

Abstract

The aim of the paper is to introduce a new similarity measure between intuitionistic fuzzy numbers (IFNs). The proposed method is based on the centroid point of IFNs. It is also proved that the proposed measure satisfies the properties of similarity measure. Examples are considered to compare the proposed similarity measure with the existing similarity measures. The similarity results show that the new similarity measure can overcome the faults of the existing similarity measures.

Keywords

Intuitionistic fuzzy number Centroid point Similarity measure 

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Dengfeng, L., Chuntian, C.: New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn. Lett. 23, 221–225 (2002)CrossRefMATHGoogle Scholar
  3. 3.
    Mitchell, H.B.: On the Dengfeng–Chuntian similarity measure and its application to pattern recognitions. Pattern Recogn. Lett. 24, 3101–3104 (2003)CrossRefGoogle Scholar
  4. 4.
    Li, Y., Zhongxian, C., Degin, Y.: Similarity measures between vague sets and vague entropy. J. Comput. Sci. 29, 129–132 (2002) (in chinese)Google Scholar
  5. 5.
    Chen, S.M.: A new approach to handling fuzzy decision making problems. IEEE Trans. Syst. Man Cybern. 18, 1012–1016 (1988)CrossRefMATHGoogle Scholar
  6. 6.
    Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern. Syst. 27, 449–472 (1996)CrossRefMATHGoogle Scholar
  7. 7.
    Hsieh, C.H., Chen, S.H.: Similarity of generalized fuzzy numbers with graded mean integration representation. In: Proceedings of the 8th International Fuzzy Systems Association World Congress, pp. 551–555. Taipei (1999)Google Scholar
  8. 8.
    Chen, S.J., Chen, S.M.: Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans. Fuzzy Syst. 11, 45–56 (2003)CrossRefGoogle Scholar
  9. 9.
    Hsu, H.M., Chen, C.T.: Aggregation of fuzzy opinions under group decision making. Fuzzy Sets Syst. 79, 279–285 (1996)Google Scholar
  10. 10.
    Lee, H.S.: An optimal aggregation method for fuzzy opinions of group decision. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 3, 314–319 (1999)Google Scholar
  11. 11.
    Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Int. J. Cybern. Syst. 27, 449–472 (1996)CrossRefMATHGoogle Scholar
  12. 12.
    Kangari, R., Riggs, L.S.: Construction risk assessment by linguistics. IEEE Trans. Eng. Manag. 36, 126–131 (1989)CrossRefGoogle Scholar
  13. 13.
    Schmucker, K.J.: Fuzzy Sets, Natural Language Computations, and Risk Analysis. Computer Science, Rockville (1984)MATHGoogle Scholar
  14. 14.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Guha, D., Chakraborty, D.: A theoretical development of similarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. J. Fuzzy Math. 18, 391–402 (2010)MATHMathSciNetGoogle Scholar
  16. 16.
    Hung, W., Yang, M.: Similarity measures of intuitionistic fuzzy sets based on Hausdroff distance. Pattern Recogn. Lett. 25, 1603–1611 (2004)CrossRefGoogle Scholar
  17. 17.
    Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114, 505–518 (2000)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Li, Y., Olson, D.L., Qin, Z.: Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recogn. Lett. 28, 278–285 (2007)CrossRefGoogle Scholar
  19. 19.
    Ye, J.: Multicriteria group decision-making method using vector similarity measure for trapezoidal intuitionistic fuzzy numbers. Group Decis. Negot. 21, 519–530 (2012)CrossRefGoogle Scholar
  20. 20.
    Ye, J.: Multicriteria group decision-making method using distance-based similarity measure for intuitionistic trapezoidal fuzzy numbers. Int. J. Gen. Syst. 41, 729–739 (2012)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Farhadinia, B., Ban, A.I.: Developing new similarity measures of generalized intuitionistic fuzzy numbers and generalized interval-valued fuzzy numbers from similarity measures of generalized fuzzy numbers. Math. Comput. Model. 57, 812–825 (2013)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Wang, J.Q., Zhang, Z.: Multi-criteria decision making method with incomplete certain information based on Intuitionistic fuzzy number. Control Decis. 24, 226–230 (2009)MATHMathSciNetGoogle Scholar
  23. 23.
    Wu, J., Cao, Q.: Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl. Math. Model. 37, 318–327 (2013)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Das, S., Guha, D.: Ranking of intuitionistic fuzzy number by centroid point. J. Ind. Intel. Inf. 1, 107–110 (2013)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Indian Institute of TechnologyPatnaIndia

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