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A generalization of the Wilcoxon signed-rank test and its applications

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Abstract

This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value.

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References

  • Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy sets. Fuzzy Sets Syst 15: 1–19

    Article  MathSciNet  MATH  Google Scholar 

  • Denoeux T, Masson MH, Herbert PH (2005) Non-parametric rank-based statistics and significance tests for fuzzy data. Fuzzy Sets Syst 153: 1–28

    Article  MATH  Google Scholar 

  • Dubois D, Prade H (1983) Ranking of fuzzy numbers in the setting of possibility theory. Inf Sci 30: 183–224

    Article  MathSciNet  MATH  Google Scholar 

  • Filzmoser P, Viertl R (2004) Testing hypotheses with fuzzy data: the fuzzy p-value. Metrika 59: 21–29

    Article  MathSciNet  MATH  Google Scholar 

  • Gibbons JD, Chakraborti S (2003) Non-parametric statistical inference, 4th edn. Marcel Dekker, New York

    Google Scholar 

  • Grzegorzewski P (1998) Statistical inference about the median from vague data. Control Cybernet 27: 447–464

    MathSciNet  MATH  Google Scholar 

  • Grzegorzewski P et al (2004) Distribution-free tests for vague data. In: Lopez-Diaz M et al (eds) Soft methodology and random information systems. Springer, Heidelberg, pp 495–502

    Google Scholar 

  • Grzegorzewski P (2005) Two-sample median test for vague data. In: Proc 4th conf. European society for fuzzy logic and technology-eusflat, Barcelona, pp 621–626

  • Grzegorzewski P (2009) K-sample median test for vague data. Int J Intel Syst 24: 529–539

    Article  MATH  Google Scholar 

  • Holena M (2004) Fuzzy hypotheses testing in a framework of fuzzy logic. Fuzzy Sets Syst 145: 229–252

    Article  MathSciNet  MATH  Google Scholar 

  • Hryniewicz O (2006) Goodman-Kruskal γ measure of dependence for fuzzy ordered categorical data. Comput Stat Data Anal 51: 323–334

    Article  MathSciNet  MATH  Google Scholar 

  • Kahraman C, Bozdag CF, Ruan D (2004) Fuzzy sets approaches to statistical parametric and non-parametric tests. Int J Intel Syst 19: 1069–1078

    Article  MATH  Google Scholar 

  • Klement EP, Puri ML, Ralescu DA (1986) Limit theorems for fuzzy random variables. Proc R Soc Lond 407: 171–482

    Article  MathSciNet  MATH  Google Scholar 

  • Kruse R, Meyer KD (1987) Statistics with vague data. Reidel Publishing Company, Dordrecht

    Book  MATH  Google Scholar 

  • Kvam PH, Vidadovic B (2007) Non-parametric statistics with application to science and engineering. Wiley, New York

    Book  Google Scholar 

  • Lee KH (2005) First course on fuzzy theory and applications. Springer, Heidelberg

    MATH  Google Scholar 

  • Lee KM, Cho CH, Hyung LK (1994) Ranking fuzzy values with satisfaction function. Fuzzy Sets Syst 64:295–309 (2005)

    Google Scholar 

  • Li S, Ogura Y (2006) Strong laws of large numbers for independent fuzzy set-valued random variables. Fuzzy Sets Syst 157: 2569–2578

    Article  MathSciNet  MATH  Google Scholar 

  • Parchami A, Taheri SM, Mashinchi M (2010) Fuzzy p-value in testing fuzzy hypotheses with crisp data. Stat Papers 51: 209–226

    Article  MathSciNet  MATH  Google Scholar 

  • Parchami A, Taheri SM, Mashinchi M (2012) Testing fuzzy hypotheses based on vague observations: a p-value approach. Stat Papers. doi:10.1007/s00362-010-0353-2

  • Puri ML, Ralescu DA (1986) Fuzzy random variables. J Math Analy Appl 114: 409–422

    Article  MathSciNet  MATH  Google Scholar 

  • Seungsoo L, Kowang H, Doheon Lee. (2004) Ranking sequenses of fuzzy values. Inf Sci 160: 41–52

    Article  MATH  Google Scholar 

  • Taheri SM, Hesamian G (2011) Goodman-Kruskal measure of association for fuzzy-categorized variables. Kybernetika 47: 110–122

    MathSciNet  MATH  Google Scholar 

  • Viertl R (2011) Statistical methods for fuzzy data. Wiley, Chichester

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    S. M. Taheri & G. Hesamian

  2. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, 91779-48974, Iran

    S. M. Taheri

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  1. S. M. Taheri
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  2. G. Hesamian
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Correspondence to S. M. Taheri.

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Taheri, S.M., Hesamian, G. A generalization of the Wilcoxon signed-rank test and its applications. Stat Papers 54, 457–470 (2013). https://doi.org/10.1007/s00362-012-0443-4

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  • DOI: https://doi.org/10.1007/s00362-012-0443-4

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