ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND THEIR MATHEMATICAL PROPERTIES

bibitem{A}
M. G. Akbari  and A. Rezaei,  {it An uniformly minimum variance unbiased point estimation using fuzzy observations}, Austrian Journal of Statistics, {bf 36} (2007), 307-317.

bibitem{B}
M. G. Akbari  and A. Rezaei,  {it Order statistics using fuzzy
random variables}, Statistics and Probability Letters, {bf 79} (2009), 1031-1037.

bibitem{au}
R. J. Aumann, {it Integrals of set-valued functions}, Journal of Mathematical Analysis and Applications, {bf 12} (1965), 1-12.

bibitem{bi}
 P. Billingsley, {it Probability and measure}, 2nd ed., New York:
John Wiley, 1995.

bibitem{ca}
J. J. Buckley, {it Fuzzy probabilities: new approach and applications}, Springer-Verlag, Berlin, Heidelberg, 2005.

bibitem{cb}
J. J. Buckley, {it Fuzzy probability and statistics}, Springer-Verlag, Berlin, Heidelberg, 2006.

bibitem{ch}
C. Cheng, {it A new approach for ranking fuzzy numbers by distance
method}, Fuzzy Sets and Systems, {bf 95} (1998), 307-317.

bibitem{g1}
G. Z. Gertner and H. Zhu, {it Bayesian estimation in forest survey
when samples or prior information are fuzzy}, Fuzzy Sets an Systems,
 {bf 77} (1997), 277-290.

bibitem{ho}
H. Hong-Zhong, J. Z. Ming  and S. Zhan-Quan, {it Bayesian
reliability analysis for fuzzy lifetime data}, Fuzzy Sets and
Systems, {bf 157} (2006), 1674-1686.

bibitem{hr}
O. Hryniewicz, {it Possibilities approach to the Bayes statistical
decisions}, In: P. Grzegorzewski, O. Hryniewicz, M. A. Gil , eds., Soft
Methods in Probability, Statistics and Data Analysis. Physica
Verlag, Heidelberg-New York, (2002), 207-218.

bibitem{k1}
R. Kruse, {it Statistical estimation with linguistic data},
Information Sciences, {bf 33} (1984), 197-207.

bibitem{k2}
R. Kruse  and K. D. Meyer, {it Statistics with vague data}, Reidel, Dordrecht, {bf 33} (1987).

bibitem{kw}
H. Kwakernaak, {it Fuzzy random variables I}, Information Sciences, {bf 15} (1978), 1-29.

bibitem{mo}
M. Modarres  and S. Sadi-Nezhad, {it Ranking fuzzy numbers by
preference ratio}, Fuzzy Sets and Systems, {bf 118} (2001), 429-436.

bibitem{na}
W. N$ddot{a}$ther, {it Regression with fuzzy data},
Computational Statistics and Data Analysis, {bf 51} (2006), 235-252.

bibitem{no}
M. Nojavan  and M. Ghazanfari, {it A fuzzy ranking method by
desirability index}, Journal of Intelligent and Fuzzy Systems,
{bf 17} (2006), 27-34.

bibitem{p1}
M. L. Puri and D. A. Ralescu, {it Differential of fuzzy functions}, Journal of Mathematical Analysis and Applications, {bf 114} (1983), 552-558.

bibitem{p2}
M. L. Puri  and D. A. Ralescu, {it Fuzzy random variables}, Journal of Mathematical Analysis and Applications, {bf 114} (1986), 409-422.

bibitem{p3}
M. L. Puri  and D. A. Ralescu, {it Convergence theorem for fuzzy martingales}, Journal of Mathematical Analysis and Applications, {bf 160} (1991), 107-122.

bibitem{sh}
J. Shao, {it Mathematical Statistics}, 2nd ed., New York:
 Springer-Verlag, 2003.

bibitem{s11}
B. Sadeghpour Gildeh  and D. Gien, {it $d_{p,q}$-distance and
Rao-Blackwell theorem for fuzzy random variables}, In Proc, of
the 8th international Conference of Fuzzy Theory and
Technology, Durham, USA, 2002.

bibitem{u1}
Y. Uemura, {it A decision rule on fuzzy events}, Japanese Journal
Fuzzy Theory and Systems, {bf 3} (1991), 291-300.

bibitem{u2}
Y. Uemura, {it A decision rule on fuzzy events under an
observation}, Journal of Fuzzy Mathematics, {bf 1} (1993), 39-52.

bibitem{v1}
R. Viertl, {it Statistical methods for non-precise data}, CRC
Press, Boca Raton, 1996.

bibitem{v2}
R. Viertl, {it Statistics with one-dimensional fuzzy data}, In C.
Bertoluzzi et al., Editor, Statistical Modeling, Analysis and
Management of Fuzzy Data, Physica-Verlag, Heidelberg, (2002a), 199-212.

bibitem{v3}
R. Viertl, {it Statistical inference with non-precise data}, In
Encyclopedia of Life Support Systems, UNESCO, Paris, 2002b.

bibitem{ac}
R. Viertl, {it Univariate statistical analysis with fuzzy data},
Computational Statistics and Data Analysis, {bf 51} (2006), 133-147.

bibitem{yaa}
J. S. Yao  and K. Wu, {it Ranking fuzzy numbers based on
decomposition  principle and signed distance}, Fuzzy Sets and Systems,  {bf 11} (2000), 275-288.