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Kendall’s correlation coefficient for vague preferences

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Abstract

The problem of measuring association between preference systems in situations with missing information or noncomparable outputs is discussed. New correlation coefficient, which generalizes Kendall’s correlation coefficients used traditionally in statistics, is suggested. The construction utilizes IF-sets.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov K (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg

  • Bromek T, Pleszczyńska E (eds) (1991) Statistical inference: theory and practice. PWN/Kluwer, Warsaw/Dordrecht

  • Chiang DA, Lin NP (1999) Correlation of fuzzy sets. Fuzzy Sets Syst 102:221–226

    Article  MATH  MathSciNet  Google Scholar 

  • Daniels HE (1950) Rank correlation and population models. J R Stat Soc Ser B 12:171–181

    MATH  MathSciNet  Google Scholar 

  • Denœux T, Masson MH, Hébert PA (2005) Nonparametric rank-based statistics and significance tests for fuzzy data. Fuzzy Sets Syst 153:1–28

    Article  MATH  Google Scholar 

  • Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  • Durbin J, Stuart A (1951) Inversions and rank correlation coefficients. J R Stat Soc Ser B 2:303–309

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Gibbons JD, Chakraborti S (2003) Nonparametric statistical inference. Marcel Dekker Inc., New York

  • Grzegorzewski P (2004) The generalized Spearman’s rank correlation coefficient. In: Proceedings of the tenth international conference on information processing and management of uncertainty in knowledge-based systems, Perugia, Italy, 4–9 July 2004, pp 1413–1418

  • Hébert PA, Masson MH, Denœux T (2003) Fuzzy rank correlation between fuzzy numbers, In: Proceedings of the tenth IFSA world congress—IFSA 2003, Istanbul, Turkey, 29 June–2 July 2003, pp 224–227

  • Hong DH (1998) A note on correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 95:113–117

    Article  MATH  Google Scholar 

  • Hong DH, Hwang SY (1995) Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets Syst 75:77–81

    Article  MATH  MathSciNet  Google Scholar 

  • Hung WL, Wu JW (2002a) A note on the correlation of fuzzy numbers by expected interval. Int J Uncertain Knowl Based Syst 9:517–523

    MathSciNet  Google Scholar 

  • Hung WL, Wu JW (2002b) Correlation of intuitionistic fuzzy sets by centroid method. Inf Sci 144:219–225

    Article  MATH  MathSciNet  Google Scholar 

  • Nelsen RB (1991) Copulas and association, In: Dall’Aglio G, Kotz S, Salinetti G (Eds) Advances in probability distributions with given marginals. Kluwer, Dordrecht, pp 51–74

  • Roy B, Słowinski R (1993) Criterion of distance between technical programing and socio-economic priority. Oper Res 27:45–60

    MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Przemysław Grzegorzewski.

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Grzegorzewski, P. Kendall’s correlation coefficient for vague preferences. Soft Comput 13, 1055–1061 (2009). https://doi.org/10.1007/s00500-008-0378-9

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  • DOI: https://doi.org/10.1007/s00500-008-0378-9

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