Abstract
This paper means an introduction to analyze whether the choice of the shape for fuzzy data in their statistical analysis can or cannot affect the conclusions of such an analysis. More concretely, samples of fuzzy data are simulated in accordance with different assumptions (distributions) concerning four relevant points (namely, those determining their core and support), and later, by preserving core and support, the ‘arms’ are changed by considering trapezoidal, Π-curves, and some LR fuzzy numbers. For the simulations obtained with each of the considered shapes, several characteristics have been estimated: Aumann-type mean, 1-norm and wabl/ldev/rdev medians and Fréchet’s variance. A comparative analysis with the bias, mean squared distance and variance of the estimates is finally included.
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References
Ban, A., Coroianu, L., Grzegorzewski, P.: Trapezoidal approximation and aggregation. Fuzzy Sets Syst. 177, 45–59 (2011)
Blanco-Fernández, A., Casals, M.R., Colubi, A., Corral, N., García-Bárzana, M., Gil, M.A., González-Rodríguez, G., López, M.T., Lubiano, M.A., Montenegro, M., Ramos-Guajardo, A.B., De la Rosa de Sáa, S., Sinova, B.: A distance-based statistical analysis of fuzzy number-valued data. Int. J. Approx. Reas (2014), doi:10.1016/j.ijar.2013.09.020
Cox, E.: The fuzzy Systems Handbook. Academic Press, Cambridge (1994)
De la Rosa de Sáa, S., Gil, M.A., González-Rodríguez, G., López, M.T., Lubiano, M.A.: Fuzzy rating scale-based questionnaires and their statistical analysis. IEEE Trans. Fuzzy Syst (2014), doi:10.1109/TFUZZ.2014.2307895
Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets. Fuzzy Sets Syst. 35, 241–249 (1990)
Grzegorzewski, P.: Trapezoidal approximations of fuzzy numbers preserving the expected interval - algorithms and properties. Fuzzy Sets Syst. 159, 1354–1364 (2008)
Grzegorzewski, P.: Fuzzy number approximation via shadowed sets. Inform. Sci. 225, 35–46 (2013)
Grzegorzewski, P., Pasternak-Winiarska, K.: Trapezoidal approximations of fuzzy numbers with restrictions on the support and core. In: Proc. 7th Conf. EUSFLAT-2011 and LFA-2011, pp. 749–756. Atlantis Press, Paris (2011)
Pedrycz, W.: Why triangular membership functions? Fuzzy Sets Syst. 64(1), 21–30 (1994)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Sinova, B., De la Rosa de Sáa, S., Gil, M.A.: A generalized L 1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data. Inform. Sci. 242, 22–34 (2013)
Sinova, B., Gil, M.A., Colubi, A., Van Aelst, S.: The median of a random fuzzy number. The 1-norm distance approach. Fuzzy Sets Syst. 200, 99–115 (2012)
Stefanini, L., Sorini, L., Guerra, M.L.: Parametric representation of fuzzy numbers and applications to fuzzy calulus. Fuzzy Sets Syst. 157, 2423–2455 (2006)
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Lubiano, M.A., de la Rosa de Sáa, S., Sinova, B., Gil, M.Á. (2015). Empirical Sensitivity Analysis on the Influence of the Shape of Fuzzy Data on the Estimation of Some Statistical Measures. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_15
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DOI: https://doi.org/10.1007/978-3-319-10765-3_15
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