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The Skorokhod topology on space of fuzzy numbers. (English) Zbl 0961.54024
The authors introduce a metric on the set \(F(\mathbb{R})\) of fuzzy numbers in the sense of R. Goetschel jun. and W. Voxman [ibid. 18, 31-43 (1986; Zbl 0626.26014)] and prove that \(F(\mathbb{R})\) with this metric becomes a Polish space.

54E35 Metric spaces, metrizability
26E50 Fuzzy real analysis
60F99 Limit theorems in probability theory
Zbl 0626.26014
Full Text: DOI
[1] Billingsley, P., Convergence of probability measures, (1968), Wiley New York · Zbl 0172.21201
[2] Congxin, W.; Ming, M., Embedding problem of fuzzy number spacepart II, Fuzzy sets and systems, 45, 189-202, (1992) · Zbl 0771.46045
[3] Daffer, P.Z.; Taylor, R.L., Laws of large numbers for \(D[0,1]\), Ann. probab., 7, 85-95, (1979) · Zbl 0402.60010
[4] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy sets and systems, 18, 31-43, (1986) · Zbl 0626.26014
[5] Jacod, J.; Shirayaev, A.N., Limit theorems for stochastic processes, (1987), Springer New York
[6] Kim, Y.K.; Ghil, B.M., Integrals of fuzzy number valued functions, Fuzzy sets and systems, 86, 213-222, (1997) · Zbl 0922.28015
[7] Klement, E.P.; Puri, M.L.; Ralescu, D.A., Limit theorems for fuzzy random variables, Proc. roy. soc. lond. ser. A, 407, 171-182, (1986) · Zbl 0605.60038
[8] Skorokhod, A.V., Limit theorems for stochastic processes, Theory probab. appl., 1, 261-290, (1956) · Zbl 0074.33802
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