Flexible resampling for fuzzy data

Ban, A., Brândaş, A., Coroianu, L., Negruţiu, C. and Nica, O. (2011). Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, Computers and Mathematics with Applications61(5): 1379–1401.10.1016/j.camwa.2011.01.005Search in Google Scholar

Ban, A., Coroianu, L. and Grzegorzewski, P. (2015). Fuzzy Numbers: Approximations, Ranking and Applications, Polish Academy of Sciences, Warsaw.Search in Google Scholar

Casals, M.R., Corral, N., Gil, M. Á., López, M.T., Lubiano, M.A., Montenegro, M., Naval, G. and Salas, A. (2013). Bertoluzza et al.’s metric as a basis for analyzing fuzzy data, METRON71(3): 307–322.Search in Google Scholar

Casella, G. (2003). Introduction to the silver anniversary of the bootstrap, Statistical Science18(2): 133–134.10.1214/ss/1063994967Search in Google Scholar

Chanas, S. (2001). On the interval approximation of a fuzzy number, Fuzzy Sets and Systems122(2): 353–356.10.1016/S0165-0114(00)00080-4Search in Google Scholar

Colubi, A. (2009). Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems160(3): 344–356.10.1016/j.fss.2007.12.019Search in Google Scholar

Colubi, A., Fernández-García, C. and Gil, M. (2002). Simulation of random fuzzy variables: An empirical approach to statistical/probabilistic studies with fuzzy experimental data, IEEE Transactions on Fuzzy Systems10(3): 384–390.10.1109/TFUZZ.2002.1006441Search in Google Scholar

Davison, A.C., Hinkley, D.V. and Schechtman, E. (1986). Efficient bootstrap simulation, Biometrika73(3): 555–566.10.1093/biomet/73.3.555Search in Google Scholar

De Angelis, D. and Young, G.A. (1992). Smoothing the bootstrap, International Statistical Review60(1): 45–56.10.2307/1403500Search in Google Scholar

Delgado, M., Vila, M. and Voxman, W. (1998). On a canonical representation of a fuzzy number, Fuzzy Sets and Systems93(1): 125–135.10.1016/S0165-0114(96)00144-3Search in Google Scholar

Denoeux, T., Masson, M.-H. and Hébert, P.-A. (2005). Nonparametric rank-based statistics and significance tests for fuzzy data, Fuzzy Sets and Systems153(1): 1–28.10.1016/j.fss.2005.01.008Search in Google Scholar

Dubois, D. and Prade, H. (1987). The mean value of a fuzzy number, Fuzzy Sets and Systems24(3): 279–300.10.1016/0165-0114(87)90028-5Search in Google Scholar

Efron, B. (1979). Bootstrap methods: Another look at the jackknife, Annals of Statistics7(1): 1–26.10.1214/aos/1176344552Search in Google Scholar

Gao, J.-Q., Fan, L.-Y., Li, L. and Xu, L.-Z. (2013). A practical application of kernel-based fuzzy discriminant analysis, International Journal of Applied Mathematics and Computer Science23(4): 887–903, DOI: 10.2478/amcs-2013-0066.10.2478/amcs-2013-0066Search in Google Scholar

Gil, M., Montenegro, M., González-Rodríguez, G., Colubi, A. and Casals, M. (2006). Bootstrap approach to the multi-sample test of means with imprecise data, Computational Statistics and Data Analysis51(1): 148–162.10.1016/j.csda.2006.04.018Search in Google Scholar

González-Rodríguez, G., Montenegro, M., Colubi, A. and Gil, M. (2006). Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data, Fuzzy Sets and Systems157(19): 2608–2613.10.1016/j.fss.2003.11.021Search in Google Scholar

Graham, R., Hinkley, D.V., John, P.W.M. and Shi, S. (1990). Balanced design of bootstrap simulations, Journal of the Royal Statistical Society B52(1): 185–202.10.1111/j.2517-6161.1990.tb01781.xSearch in Google Scholar

Grzegorzewski, P. (2008). Trapezoidal approximations of fuzzy numbers preserving the expected interval—Algorithms and properties, Fuzzy Sets and Systems159(11): 1354–1364.10.1016/j.fss.2007.12.001Search in Google Scholar

Grzegorzewski, P. (2018). The Kolmogorov–Smirnov goodness-of-fit test for interval-valued data, in E. Gil et al. (Eds), The Mathematics of the Uncertain: A Tribute to Pedro Gil, Springer International Publishing, Cham, pp. 615–627.10.1007/978-3-319-73848-2_57Search in Google Scholar

Grzegorzewski, P. and Hryniewicz, O. (2002). Computing with words and life data, International Journal of AppliedMathematics and Computer Science12(3): 337–345.Search in Google Scholar

Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2019). Flexible bootstrap based on the canonical representation of fuzzy numbers, Proceedings of EUSFLAT 2019, Prague, Czech Republic, pp. 490–497.Search in Google Scholar

Hall, P., DiCiccio, T. and Romano, J. (1989). On smoothing and the bootstrap, Annals of Statistics17(2): 692–704.10.1214/aos/1176347135Search in Google Scholar

Heilpern, S. (1992). The expected value of a fuzzy number, Fuzzy Sets and Systems47(1): 81–86.10.1016/0165-0114(92)90062-9Search in Google Scholar

Jimenez, M. and Rivas, J.A. (1998). Fuzzy number approximation, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems6(1): 68–78.10.1142/S0218488598000057Search in Google Scholar

Lubiano, M.A., Montenegro, M., Sinova, B., de la Rosa de Sáa, S. and Gil, M.A. (2016). Hypothesis testing for means in connection with fuzzy rating scale-based data: Algorithms and applications, European Journal of Operational Research251(3): 918–929.10.1016/j.ejor.2015.11.016Search in Google Scholar

Lubiano, M.A., Salas, A., Carleos, C. and de la Rosa de Sáa, S.and Gil, M.A. (2017). Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning88: 128–147.10.1016/j.ijar.2017.05.007Search in Google Scholar

Montenegro, M., Colubi, A., Casals, M. and Gil, M. (2004). Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika59(1): 31–49.10.1007/s001840300270Search in Google Scholar

Pedrycz, W. (1994). Why triangular membership functions?, Fuzzy Sets and Systems64(1): 21–30.10.1016/0165-0114(94)90003-5Search in Google Scholar

Puri, M. and Ralescu, D.A. (1986). Fuzzy random variables, Journal of the Mathematical Analysis and Applications114(2): 409–422.10.1016/0022-247X(86)90093-4Search in Google Scholar

Ramos-Guajardo, A., Blanco-Fernández, A. and González-Rodríguez, G. (2019). Applying statistical methods with imprecise data to quality control in cheese manufacturing, in P. Grzegorzewski et al. (Eds), Soft Modeling in Industrial Manufacturing, Springer, Cham, pp. 127–147.10.1007/978-3-030-03201-2_8Search in Google Scholar

Ramos-Guajardo, A. and Grzegorzewski, P. (2016). Distance-based linear discriminant analysis for interval-valued data, Information Sciences372: 591–607.10.1016/j.ins.2016.08.068Search in Google Scholar

Ramos-Guajardo, A. and Lubiano, M. (2012). k-Sample tests for equality of variances of random fuzzy sets, Computational Statistics and Data Analysis56(4): 956–966.10.1016/j.csda.2010.11.025Search in Google Scholar

Romaniuk, M. (2019). On some applications of simulations in estimation of maintenance costs and in statistical tests for fuzzy settings, in A. Steland et al. (Eds), Stochastic Models, Statistics and Their Applications, Springer International Publishing, Cham, pp. 437–448.10.1007/978-3-030-28665-1_33Search in Google Scholar

Romaniuk, M. and Hryniewicz, O. (2019a). Discrete and smoothed resampling methods for interval-valued fuzzy numbers, IEEE Transactions on Fuzzy Systems, DOI: 10.1109/TFUZZ.2019.2957253, (in press).10.1109/TFUZZ.2019.2957253Search in Google Scholar

Romaniuk, M. and Hryniewicz, O. (2019b). Interval-based, nonparametric approach for resampling of fuzzy numbers, Soft Computing23(14): 5883–5903.10.1007/s00500-018-3251-5Search in Google Scholar

Silverman, B.W. and Young, G.A. (1987). The bootstrap: To smooth or not to smooth?, Biometrika74(3): 469–479.10.1093/biomet/74.3.469Search in Google Scholar

Sinova, B., Gil, M.A., Colubi, A. and Aelst, S.V. (2012). The median of a random fuzzy number. The 1-norm distance approach, Fuzzy Sets and Systems200: 99–115.Search in Google Scholar

Wang, D. and Hryniewicz, O. (2015). A fuzzy nonparametric Shewhart chart based on the bootstrap approach, International Journal of Applied Mathematics and Computer Science25(2): 389–401, DOI: 10.1515/amcs-2015-0030.10.1515/amcs-2015-0030Search in Google Scholar