An Uniformly Minimum Variance Unbiased Point Estimator Using Fuzzy Observations
DOI:
https://doi.org/10.17713/ajs.v36i4.341Abstract
This paper proposes a new method for uniformly minimum variance unbiased fuzzy point estimation. For this purpose we make use of a uniformly minimum variance unbiased estimator and we develop this new method for a fuzzy random sample ~X1,...,~Xn is induced by X1,,...,Xn onthe same probability space.
References
Billingsley, P. (1995). Probability and Measure (2nd ed.). New York: John Wiley.
Buckley, J. J. (1983). Fuzzy decision making with data: applications to statistics. Fuzzy Sets and Systems, 16, 139-174.
Cai, K. Y. (1993). Parameter estimation of normal fuzzy variables. Fuzzy Sets and Systems, 55, 179-185.
Cai, K. Y., Wen, C. Y., and Zhang, M. L. (1991). Fuzzy variable as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets and Systems, 42, 145-172.
Cheng, C.(1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95, 307-317.
Garcia, D., Lubiano, M. A., and Alonso, C. (2001). Estimating the expected value of fuzzy random variables in the stratified random sampling from finite populations.
Information Sciences, 138, 165-184.
Gertner, G. Z., and Zhu, H.(1997). Bayesian estimation in forest survey when samples or prior information are fuzzy. Fuzzy Sets and Systems, 77, 277-290.
Hong-Zhong, H., Ming, J. Z., and Zhan-Quan, S.(2006). Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets and Systems, 157, 1674-1686.
Hryniewicz, O.(2002). Possibilities approach to the Bayes statistical decisions. In P. Grzegorzewski, O. Hryniewicz, and M. A. Gil (Eds.), Soft Methods in Probability, Statistics
and Data Analysis (p. 207-218). Heidelberg-New York: Physica Verlag.
Klir, G., and Yuan, B. (1995). Fuzzy sets and fuzzy logic-theory and applications. Upper Saddle River, NJ: Prentice-Hall.
Kruse, R. (1984). Statistical estimation with linguistic data. Information Science, 33, 197-207.
Kruse, R., and Meyer, K. D. (1987). Statistics with Vague Data (Vol. 33). Dordrecht: Reidel.
Lopez-Diaz, M., and Gil, M. A. (1998). Reversing the order of integration in iterated expectations of fuzzy random variables, and statistical applications. Jornal of Statistical
Planning and Inference, 74, 11-29.
Lubiano, M. A., Gil, M. A., and Lopez-Diaz, M. (1999). On the Rao-Blackwell theorem for fuzzy random variables. Kybernetica, 35, 167-175.
Modarres, M., and Sadi-Nezhad, S. (2001). Ranking fuzzy numbers by preference ratio. Fuzzy Sets and Systems, 118, 429-436.
Nojavan, M., and Ghazanfari, M. (2006). A fuzzy ranking method by desirability index. Journal of Intelligent and Fuzzy Systems, 17, 27-34.
Okuda, T. (1987). A statistical treatment of fuzzy observations: estimation problems. In Preprints of the 2nd IFSA Congress (p. 51-55).
Sadeghpour, G. B., and Gien, D. (2002). dp;q-distance and Rao-Blackwell theorem for fuzzy random variables. In Proceedings of the 8th international Conference of Fuzzy Theory and Technology. Durham, USA.
Shao, J. (2003). Mathematical Statistics (2nd ed.). New York: Springer-Verlag.
Uemura, Y. (1991). A decision rule on fuzzy events. Japanese Journal of Fuzzy Theory and Systems, 3, 291-300.
Uemura, Y. (1993). A decision rule on fuzzy events under an observation. Journal of Fuzzy Mathematics, 1, 39-52.
Viertl, R.(1996). Statistical Methods for Non-Precise Data. Boca Raton: CRC Press.
Viertl, R.(2002a). Statistics with one-dimensional fuzzy data. In C. B. et al. (Ed.), Statistical Modeling, Analysis and Management of Fuzzy Data (p. 199-212). Heidelberg:
Physica-Verlag.
Viertl, R. (2002b). Statistical inference with non-precise data. In Encyclopedia of Life Support Systems. Paris: UNESCO.
Wu, H. C. (2003). The fuzzy estimators of fuzzy parameters based on fuzzy random variables. European Journal of Operation Research, 146, 101-114.
Yao, J. S., and Wu, K.(2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, 11, 275-288.
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