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Fuzzy decision in testing hypotheses by fuzzy data: two case studies. (English) Zbl 1458.62082

Summary: In testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of testing hypotheses are not capable and need to be generalized. In solving the problem of testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy \(p\)-value. This paper has been focused to calculate fuzzy \(p\)-value based on fuzzy data using the extension principle. Also, considering that \(p\)-value method is the most widely used / popular approach for testing hypotheses among different sciences users, two fuzzy \(p\)-value-based case studies have been provided in this paper. The first case study is discussed on “the fuzzy data from a speedometer camera” and the second is deliberate about “the lifetime of produced batteries in a factory” and both of them have been solved by a novel approach considering other studies found in the literature.

MSC:

62F86 Parametric inference and fuzziness
62F03 Parametric hypothesis testing
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[1] A. Blanco-Fern´andez, M. R. Casals, A. Colubi, N. Corral, M. Garca-Brzana, M. A. Gil, G. Gonz´alez-Rodriguez, M. T. L´opez, M. A. Lubiano, M. Montenegro, A. B. Ramos-Guajardo, S. de la Rosa de Sa, B. Sinova,Random fuzzy sets: A mathematical tool to develop statistical fuzzy data analysis, Iranian Journal of Fuzzy Systems,10(2013), 1-28. · Zbl 1331.62055
[2] M. R. Casals, M. A. Gil, P. Gil,On the use of Zadehs probabilistic definition for testing statistical hypotheses from fuzzy information, Fuzzy Sets and Systems,20(1986), 175-190. · Zbl 0611.62018
[3] G. Casella, R. L. Berger,Statistical inference, Brooks/Cole Publishing, Belmont, 1990. · Zbl 0699.62001
[4] J. Chachi, S. M. Taheri, R. Viertl,Testing statistical hypotheses based on fuzzy confidence intervals, Austrian Journal of Statistics,41(2012), 267-286.
[5] T. Deoeux, M. H. Masson, P. A. H´ebert,Nonparametric rank-based statistics and significance tests for fuzzy data, Fuzzy Sets and Systems,153(2005), 1-28. · Zbl 1062.62075
[6] D. Dubois, H. Prade,Possibility theory, Plenum Press, New-York, 1988. · Zbl 0645.68108
[7] P. Filzmoser, R. Viertl,Testing hypotheses with fuzzy data: The fuzzyp-value, Metrika,59(2004), 21-29. · Zbl 1052.62009
[8] M. Gagolewski, J. Caha,Fuzzy numbers package: Tools to deal with fuzzy numbers inR,Rpackage version 0.4-1 (2015). https://cran.r-project.org/web/packages=FuzzyNumbers
[9] P. Grzegorzewski, A. Jedrej,Chi-square goodness-of-fit test for vague data, in: Proceedings of the Eleventh International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems - IPMU 2006, Paris (2006), 952-956.
[10] P. Grzegorzewski, H. Szymanowski,Goodness-of-fit tests for fuzzy data, Information Sciences,288(2014), 374-386. · Zbl 1357.62218
[11] G. Hesamian, S. M. Taheri,Fuzzy empirical distribution function: Properties and application, Kybernetika,49 (2013), 962-982. · Zbl 1284.93240
[12] O. Hryniewicz,Statistical properties of the fuzzyp-value, International Journal of Approximate Reasoning,93 (2018), 544-560. · Zbl 1458.62081
[13] C. Kahraman, C. E. Bozdag, D. Ruan, A. F. ¨Ozok,Fuzzy set approaches to statistical parametric and nonparametric tests, International Journal Of Intelligent Systems,19(2004), 1069-1087. · Zbl 1074.62029
[14] C. Kahraman, ¨O. Kabak,Fuzzy statistical decision-making: Theory and applications, Chapters in Springer International Publishing Switzerland,343(2016). · Zbl 1360.62015
[15] A.Parchami,Fuzzy.p.value:Computingfuzzyp-value,Rpackageversion1.0,(2016).URL: https://CRAN.Rproject.org/package=Fuzzy.p.value.
[16] A. Parchami,FPV: Testing hypotheses via fuzzyp-value in fuzzy environment,Rpackage version 0.5, (2017). URL: https://CRAN.R-project.org/package=FPV.
[17] A. Parchami,Fuzzy decision making in testing hypotheses:An introduction to the packages “FPV” and “Fuzzy.p.value” with practical examples, Iranian Journal of Fuzzy Systems, (2019). DOI: 10.22111/IJFS.2019.4878
[18] A. Parchami, S. M. Taheri, M. Mashinchi,Fuzzyp-value in testing fuzzy hypotheses with crisp data, Statistical Papers,51(2010), 209-226. · Zbl 1247.62105
[19] A. Parchami, S. M. Taheri, M. Mashinchi,Testing fuzzy hypotheses based on vague observations: Ap-value approach, Statistical Papers,53(2012), 469-484. · Zbl 1440.62104
[20] A. Parchami, S. M. Taheri, B. Sadeghpour-Gildeh, M. Mashinchi,A simple but efficient approach for testing fuzzy hypotheses, Journal of Uncertainty Analysis and Applications, Springer,4(2) (2016), 1-16. · Zbl 1367.62042
[21] A. Parchami, S. T. Taheri, B. Sadeghpour Gildeh, M. Mashinchi,Testing fuzzy hypotheses: A newp-value-based approach, C. Kahraman and O. Kabak (eds.), Fuzzy Statistical Decision-Making: Theory and Applications, Springer International Publishing Switzerland,343(2016), 155-173. · Zbl 1367.62042
[22] A. Parchami, S. M. Taheri, R. Viertl, M. Mashinchi,Minimax test for fuzzy hypotheses · Zbl 1408.62051
[23] S. M. Taheri,Trends in fuzzy statistics, Austrian Journal of Statistics,32(2003), 239-257.
[24] S. M. Taheri, J. Behboodian,Neyman-pearson lemma for fuzzy hypotheses testing, Metrika,49(1999), 3-17. · Zbl 1093.62520
[25] H. Torabi, J. Behboodian,Sequential probability ratio test for fuzzy hypotheses testing with vague data, Austrian Journal of Statistics,34(2005), 25-38.
[26] R. Viert,Statistical methods for fuzzy data, Wiley, Chichester, 2011. · Zbl 1278.62014
[27] X. Wang, E. E. Kerre,Reasonable properties for the ordering of fuzzy quantities (II), Fuzzy Sets and Systems,118 (2001), 387-405. · Zbl 0971.03055
[28] Y. Yuan,Criteria for evaluating fuzzy ranking methods, Fuzzy Sets and Systems,43(1991), 139-157. · Zbl 0747.90003
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