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Similarity Measure of Intuitionistic Fuzzy Numbers by the Centroid Point

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Book cover Mathematics and Computing 2013

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dengfeng, L., Chuntian, C.: New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn. Lett. 23, 221–225 (2002)

    Article  MATH  Google Scholar 

  3. Mitchell, H.B.: On the Dengfeng–Chuntian similarity measure and its application to pattern recognitions. Pattern Recogn. Lett. 24, 3101–3104 (2003)

    Article  Google Scholar 

  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. Chen, S.M.: A new approach to handling fuzzy decision making problems. IEEE Trans. Syst. Man Cybern. 18, 1012–1016 (1988)

    Article  MATH  Google Scholar 

  6. Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern. Syst. 27, 449–472 (1996)

    Article  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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. Chen, S.M.: New methods for subjective mental workload assessment and fuzzy risk analysis. Int. J. Cybern. Syst. 27, 449–472 (1996)

    Article  MATH  Google Scholar 

  12. Kangari, R., Riggs, L.S.: Construction risk assessment by linguistics. IEEE Trans. Eng. Manag. 36, 126–131 (1989)

    Article  Google Scholar 

  13. Schmucker, K.J.: Fuzzy Sets, Natural Language Computations, and Risk Analysis. Computer Science, Rockville (1984)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  16. Hung, W., Yang, M.: Similarity measures of intuitionistic fuzzy sets based on Hausdroff distance. Pattern Recogn. Lett. 25, 1603–1611 (2004)

    Article  Google Scholar 

  17. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114, 505–518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  19. Ye, J.: Multicriteria group decision-making method using vector similarity measure for trapezoidal intuitionistic fuzzy numbers. Group Decis. Negot. 21, 519–530 (2012)

    Article  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  23. Wu, J., Cao, Q.: Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl. Math. Model. 37, 318–327 (2013)

    Article  MathSciNet  Google Scholar 

  24. Das, S., Guha, D.: Ranking of intuitionistic fuzzy number by centroid point. J. Ind. Intel. Inf. 1, 107–110 (2013)

    Google Scholar 

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Authors and Affiliations

  1. Indian Institute of Technology, Patna, 800013, India

    Satyajit Das & Debashree Guha

Authors
  1. Satyajit Das
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  2. Debashree Guha
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Corresponding author

Correspondence to Debashree Guha .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  2. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. Ministry of Defence, Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, Delhi, India

    P. K. Saxena

  4. Department of Mathematics, India Institute of Technology, Kharagpur, West Bengal, India

    P. D. Srivastava

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Das, S., Guha, D. (2014). Similarity Measure of Intuitionistic Fuzzy Numbers by the Centroid Point. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_15

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