Abstract
In this communication we present a procedure to test whether the variance of a fuzzy random variable (FRV) is a given value or not by using asymptotic techniques. The variance considered here is defined in terms of a generalized metric in order to quantify the variability of the fuzzy values of the FRV about its expected value. We present some simulations to show the empirical behavior of the test in different situations and an illustrative example to demonstrate its use in practice.
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Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware Soft. Comput. 2, 71–84 (1995)
Colubi, A., Domínguez-Menchero, J.S., López-Díaz, M., Ralescu, R.: A \(D\sb E[0,1]\) representation of random upper semicontinuous functions. Proc. Amer. Math. Soc. 130, 3237–3242 (2002)
Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific Publishing Co., Inc., River Edge (1994)
Gil, M.A., Montenegro, M., González-Rodríguez, G., Colubi, A., Casals, M.R.: Bootstrap approach to the multi-sample test of means with imprecise data. Comput. Statist. Data Anal. 51, 148–162 (2006)
Giné, E., Zinn, J.: Bootstraping general empirical measures. Ann. Probab. 18, 851–869 (1990)
González-Rodríguez, G., Montenegro, M., Colubi, A., Gil, M.A.: Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data. Fuzzy Sets Syst. 157(19), 2608–2613 (2006)
Klement, E., Puri, M.L., Ralescu, D.A.: Limit theorems for fuzzy random variables. Proc. R. Soc. Lond A. 407, 171–182 (1986)
Körner, R.: An asymptotic α-test for the expectation of random fuzzy variables. J. Statist. Plann. Inference 83, 331–346 (2000)
Körner, R., Näther, W.: On the variance of random fuzzy variables. In: Bertoluzza, C., Gil, M.A., Ralescu, D.A. (eds.) Statistical Modeling, Analysis and Management of Fuzzy Data. Studies in Fuzziness and Soft Computing, vol. 87, pp. 22–39. Physica-Verlag, Heildelberg (2002)
Lubiano, M.A.: Medidas de Variación para Elementos Aleatorios Imprecisos. PhD Thesis, University of Oviedo (1999)
Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59, 31–49 (2004)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Ramos, A.B., González-Rodríguez, G., Gil, M.A., Colubi, A.: One-sample bootstrap tests for the variance of a fuzzy random variable. (submitted for publication) (2008)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part 1. Inform. Sci. 8, 199–249; Part 2. Inform. Sci. 8, 301–353; Part 3. Inform. Sci. 9, 43–80 (1975)
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Ramos, A.B., González-Rodríguez, G., Colubi, A., Gil, M.Á. (2008). Asymptotic Tests for the Variance of a Fuzzy Random Variable Using the D K -Metric. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_18
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DOI: https://doi.org/10.1007/978-3-540-85027-4_18
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