The stability of parameter estimation of fuzzy variables
Kybernetika, Tome 45 (2009) no. 3, pp. 529-540 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Recently, the parameter estimations for normal fuzzy variables in the Nahmias' sense was studied by Cai [4]. These estimates were also studied for general $T$-related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.
Recently, the parameter estimations for normal fuzzy variables in the Nahmias' sense was studied by Cai [4]. These estimates were also studied for general $T$-related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.
Classification : 03E72, 28E10, 62F86, 62L12
Keywords: duzzy variables; parameter estimation; consistency; MSE; stability of estimation
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     author = {Hong, Dug Hun},
     title = {The stability of parameter estimation of fuzzy variables},
     journal = {Kybernetika},
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     zbl = {1173.28306},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a10/}
}
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Hong, Dug Hun. The stability of parameter estimation of fuzzy variables. Kybernetika, Tome 45 (2009) no. 3, pp. 529-540. http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a10/

[1] R. Badard: The law of large numbers for fuzzy processes and the estimation problem. Inform. Sci. 28 (1982), 161–178. | MR | Zbl

[2] K. Y. Cai, C. Y. Wen, and M. L. Zhang: Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets and Systems 42 (1991), 145–172. | MR

[3] K. Y. Cai, C. Y. Wen, and M. L. Zhang: Possibistic reliability behavior of typical systems with two types of failures. Fuzzy Sets and Systems 43 (1991), 17–32. | MR

[4] K. Y. Cai: Parameter estimations of normal fuzzy variables. Fuzzy Sets and Systems 55 (1993), 179–185. | MR

[5] S. Chanas and M. Nowakowski: Single value simulation of fuzzy variable. Fuzzy Sets and Systems 25 (1988), 43–59. | MR

[6] H. Dishkant: About membership functions estimation. Fuzzy Sets and Systems 5 (1981), 141–147. | MR | Zbl

[7] D. Dubois and H. Prade: Additions of interactive fuzzy numbers. IEEE Trans. Automat. Control 26 (1981), 926–936. | MR

[8] D. Dubois and H. Prade: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York 1980. | MR

[9] S. Heilpern: The expected value of a fuzzy number. Fuzzy Sets and Systems 47 (1992), 81–86. | MR | Zbl

[10] D. H. Hong: Parameter estimations of mutually $T$-related fuzzy variables. Fuzzy Sets and Systems 123 (2001), 63–71. | MR | Zbl

[11] D. H. Hong: A note on $t$-norm-based addition of fuzzy intervals. Fuzzy Sets and Systems 75 (1995), 73–76. | MR | Zbl

[12] D. H. Hong and Hoyong Kim: A note to sum of fuzzy variables. Fuzzy Sets and Systems 93 (1998), 121–124. | MR

[13] D. H. Hong and P. I. Ro: The law of large numbers for fuzzy numbers with unbounded supports. Fuzzy Sets and Systems 116 (2000), 269–274. | MR

[14] D. H. Hong and C. Hwang: $T$-sum bound of $LR$-fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 239–252. | MR

[15] D. H. Hong and J. Lee: On the law of large numbers for mutually $T$-related $L$-$R$ fuzzy numbers. Fuzzy Sets and Systems 116 (2000), 263–269. | MR

[16] A. Marková: $T$-sum of $LR$-fuzzy numbers. Fuzzy Sets and Systems 85 (1996), 379–384. | MR

[17] R. Mesiar: Triangular norm-based additions of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 231–237. | MR

[18] S. Nahmias: Fuzzy variables. Fuzzy Sets and Systems 1 (1978), 97–110. | MR | Zbl

[19] H. T. Nguyen: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64 (1978), 369–380. | MR | Zbl

[20] M. B. Rao and A. Rashed: Some comments on fuzzy variables. Fuzzy Sets and Systems 6 (1981), 285–292. | MR

[21] B. Schweizer and A. Sklar: Probabilistic Metric Space. North-Holland, New York 1983. | MR

[22] P. Z. Wang: Fuzzy Set Theory and Its Applications. Shanghai Publishing House of Science and Technology, Shanghai 1983. | MR

[23] L. A. Zadeh: Fuzzy Sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3–28. | MR | Zbl