Ghil, Byung Moon; Joo, Sang Yeol; Kim, Yun Kyong A characterization of compact subsets of fuzzy number space. (English) Zbl 1004.54009 Fuzzy Sets Syst. 123, No. 2, 191-195 (2001). Summary: A characterization of compact subsets on the space of fuzzy numbers endowed with the Skorokhod topology is presented. This characterization is an analogue of the Arzela-Ascoli theorem which characterizes compact subsets of the space \(C[0,1]\). Cited in 7 Documents MSC: 54A40 Fuzzy topology 54C35 Function spaces in general topology Keywords:fuzzy numbers; Skorokhod topology; compact subsets PDFBibTeX XMLCite \textit{B. M. Ghil} et al., Fuzzy Sets Syst. 123, No. 2, 191--195 (2001; Zbl 1004.54009) Full Text: DOI References: [1] Billingsley, P., Convergence of Probability Measures (1968), Wiley: Wiley New York · Zbl 0172.21201 [2] Congxin, Wu; Ming, Ma, Embedding problem of fuzzy number spacePart II, Fuzzy Sets and Systems, 45, 189-202 (1992) · Zbl 0771.46045 [3] Diamond, P.; Kloeden, P., Characterization of compact subsets of fuzzy sets, Fuzzy Sets and Systems, 29, 341-348 (1989) · Zbl 0661.54011 [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: Springer New York [6] Joo, S. Y.; Kim, Y. K., The Skorokhod topology on space of fuzzy numbers, Fuzzy Sets and Systems, 111, 497-501 (2000) · Zbl 0961.54024 [7] Kim, Y. K.; Ghil, B. M., Integrals of fuzzy number valued functions, Fuzzy Sets and Systems, 86, 213-222 (1997) · Zbl 0922.28015 [8] Klement, E. P.; Puri, M. L.; Ralescu, D. A., Limit theorems for fuzzy random variables, Proc. Roy. Soc. London Ser. A, 407, 171-182 (1986) · Zbl 0605.60038 [9] Skorokhod, A. V., Limit theorems for stochastic processes, Theory Probab. Appl., 1, 261-290 (1956) · Zbl 0074.33802 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.