Abstract
In functional issues, due to lack of precise information and hypotheses and enough assumptions about distribution or the population parameters, the fuzzy nonparametric tests are used. Regarding the fact that the nonparametric tests are based upon ranking observations, it is important to rank the fuzzy observations in order to do nonparametric tests. In this article, a method of ranking fuzzy data is offered based on the D p,q —distance between two fuzzy numbers and the results of this method are evaluated and compared with other methods. When the data and hypotheses are not precise, the presented method is used to do nonparametric tests related to the median in one or two populations. Finally, some applied examples in management, psychology, and lifetime testing are provided to illustrate the efficiency of proposed approaches. Moreover, the proposed methods are examined to compare with some other existing methods and their effectiveness will be cleared via some numerical examples and some comparison studies.
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References
Arefi, M., Taheri, S.M.: Testing fuzzy hypotheses using fuzzy data based on fuzzy test statistic. J. Uncertain Syst. 5(1), 45–61 (2011)
Dat, L.Q., Yu, V.F., Chou, S.Y.: An improved ranking method for fuzzy numbers based on the centroid- index. Int. J. Fuzzy Syst. 14(3), 413–419 (2012)
Denoeux, T., Masson, M.H., Herbert, P.A.: Non-parametric rank based statistics and significance test for fuzzy data. Fuzzy Sets Syst. 153, 1–28 (2005)
Dubois, D., Prade, H.: Ranking of fuzzy numbers in the setting of possibility theory. Inform. Sci. 30, 183–224 (1983)
Gibbons, J.D., Chakraborti, S.: Non-parametric Statistical Inference, Forth edn. Marcel Dekker, New York (2003)
Grzegorzewski, P.: A bi- robust tesr for vague data. In: Magdalana L., Ojeda-Aciego M., Verdegay J.L. (eds.) Proceedings of 12th International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems, IPMU2008, pp. 138–144. Torremolinos, Malaga (2008)
Grzegorzewski, P.: Statistical inference about the median from vague data. Control Cybern. 27, 447–464 (1998)
Grzegorzewski, P.: Distribution-Free Tests for Vague Data, Soft Methodology and Random Information Systems. Springer, Heidelberg (2004)
Grzegorzewski, P.: Two-sample median test for vague data. Proceedings of 4th Conference European Society for Fuzzy Logic and Technology-Eusflat, pp. 621–626. Barcelona (2005)
Hesamian, G., Taheri, S.M.: Linear rank test for two-sample fuzzy data: a p-value approach. J. Uncertain Syst. 7(2), 129–137 (2013)
Hesamian, G., Chachi, J.: Fuzzy sign test for imprecise quantities: a p-value approach. J. Intell. Fuzzy Syst. 27, 3159–3167 (2014)
Kahraman, C., Bozdag, D., Ruan, D., Ozok, A.F.: Fuzzy sets approaches to statistical parametric and non-parametric tests. Int. J. Intell. Syst. 19, 1069–1078 (2004)
KaLpanapriya, D., Pandian, P.: Two- sample statistical hypotheses test for means with imprecise data. Int. J. Eng. Res. Appl. 2(3), 3210–3217 (2012)
Perolat, J., Couso, I., Loquin, K., Strauss, O.: Generalizing the Wilcoxon rank-sum test for interval data. Int. J. Approx. Reason. 56, 108–121 (2015)
Lee, K.H.: First Course on Fuzzy Theory and Applications. Springer, Heidelberg (2005)
Lin, G.R.: Fuzzy sampling survey with nonparametric tests. http://nccuir.lib.nccu.edu.tw/handle/140.119/39408 (2006)
Sadeghpour Gildeh, B., Gien, D.: D p,q distance and the correlation coefficient between two fuzzy random variables. Rencontres Franceophones sur la logique floue et ses applications, pp. 97–101. Mons (2001)
Taheri, S.M., Hesamian, G.: A Generalization of the Wilcoxon signed-rank test and its application. Stat. Papers 54(2), 457–470 (2013)
Wu, H.C.: Statistical hypotheses testing for fuzzy data. Inform. Sci. 175, 30–56 (2005)
Yao, J.S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets Syst. 116, 275–288 (2000)
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Momeni, F., Gildeh, B.S. Nonparametric Tests for Median in Fuzzy Environment. Int. J. Fuzzy Syst. 18, 130–139 (2016). https://doi.org/10.1007/s40815-015-0107-3
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DOI: https://doi.org/10.1007/s40815-015-0107-3