Feng, Yuhu Gaussian fuzzy random variables. (English) Zbl 0966.60017 Fuzzy Sets Syst. 111, No. 3, 325-330 (2000). M. L. Puri and D. A. Ralescu [Ann. Probab. 13, 1373-1379 (1985; Zbl 0583.60011)] introduced the concept of Lipschitzian Gaussian fuzzy random variables (f.r.v.) and proved the following representation theorem: Every Gaussian f.r.v. equals the sum of its expectation and a mean zero Gaussian random vector. Using M. Ma’s more general embedding theorem [Fuzzy Sets Syst. 55, No. 3, 313-318 (1993; Zbl 0798.46058)] the author proves the same representation theorem for Gaussian f.r.v. but without Lipschitz condition. Moreover, the covariance operator, the characteristic functional and linear transformations of Gaussian f.r.v. are introduced and investigated. Reviewer: Wolfgang Näther (Freiberg) Cited in 13 Documents MSC: 60E99 Distribution theory 03E72 Theory of fuzzy sets, etc. Keywords:Gaussian fuzzy random variable; covariance operator; characteristic functional Citations:Zbl 0583.60011; Zbl 0798.46058 PDFBibTeX XMLCite \textit{Y. Feng}, Fuzzy Sets Syst. 111, No. 3, 325--330 (2000; Zbl 0966.60017) Full Text: DOI References: [1] Diamond, P.; Kloeden, P., Metric space of fuzzy sets, Fuzzy Sets and Systems, 35, 241-249 (1990) · Zbl 0704.54006 [2] Feng, Y., Convergence theorems for fuzzy random variables and fuzzy martingales, Fuzzy Sets and Systems, 103, 435-441 (1999) · Zbl 0939.60027 [3] Frechet, M., Generalization de la loi de probabilite de Laplace, Ann. Inst. H. Poincare, 12, 215-310 (1951) [4] Ma, M., On embedding problems of fuzzy number space: part 5, Fuzzy Sets and Systems, 55, 313-318 (1993) · Zbl 0798.46058 [5] Nguyen, H. T., A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64, 369-380 (1978) · Zbl 0377.04004 [6] Puri, M. L.; Ralescu, D. A., The concept of normality of fuzzy random variables, Ann. Probab., 13, 1373-1379 (1985) · Zbl 0583.60011 [7] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, Second Printing, 1972.; R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, Second Printing, 1972. · Zbl 0224.49003 [8] Rudin, W., Functional Analysis (1973), McGraw-Hill: McGraw-Hill New York · Zbl 0253.46001 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.