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On Correlation Measures of Intuitionistic Fuzzy Sets

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4224))

Abstract

The intuitionistic fuzzy set, developed by Atanassov [1], is a useful tool to deal with vagueness and uncertainty.Correlation analysis of intuitionistic fuzzy sets is an important research topic in the intuitionistic fuzzy set theory and has great practical potential in a variety of areas, such as engineering, decision making, medical diagnosis, pattern recognition, etc. In this paper, we propose a new method for deriving the correlation coefficients of intuitionistic fuzzy sets, which has some advantages over the existing methods. Furthermore, we extend the developed method to the interval-valued intuitionistic fuzzy set theory, and show its application in medical diagnosis.

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References

  • Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  • Deschrijver, G., Kerre, E.E.: On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems 136, 333–361 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Deschrijver, G., Kerre, E.E.: On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems 12, 45–61 (2004)

    Article  Google Scholar 

  • Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31, 343–349 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, S.M., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67, 163–172 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114, 103–113 (2000)

    Article  MATH  Google Scholar 

  • Atanassov, K., Georgiev, C.: Intuitionistic fuzzy prolog. Fuzzy Sets and Systems 53, 121–128 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  • De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117, 209–213 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Szmidt, E., Kacprzyk, J.: A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 388–393. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  • Liang, Z.Z., Shi, P.F.: Similarity measures on intuitionistic fuzzy sets. Pattern Recognition letters 24, 2687–2693 (2003)

    Article  MATH  Google Scholar 

  • Gerstenkorn, T., Manko, J.: Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems 44, 39–43 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • Hong, D.H., Hwang, S.Y.: Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets and Systems 75, 77–81 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • Hung, W.L.: Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets. International Journal of Uncertainty Fuzziness Knowledge-Based Systems 9, 509–516 (2001)

    MATH  MathSciNet  Google Scholar 

  • Mitchell, H.B.: A correlation coefficient for intuitionistic fuzzy sets. International Journal of Intelligent Systems 19, 483–490 (2004)

    Article  MATH  Google Scholar 

  • Hung, W.L., Wu, J.W.: Correlation of intuitionistic fuzzy sets by centroid method. Information Sciences 144, 219–225 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Bustince, H., Burillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 74, 237–244 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • Hong, D.H.: A note on correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 95, 113–117 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Xu, Z. (2006). On Correlation Measures of Intuitionistic Fuzzy Sets. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2006. IDEAL 2006. Lecture Notes in Computer Science, vol 4224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875581_2

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  • DOI: https://doi.org/10.1007/11875581_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45485-4

  • Online ISBN: 978-3-540-45487-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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