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A stong law of large numbers for fuzzy random variables. (English) Zbl 0967.60029

For random fuzzy numbers which are levelwise independent and levelwise identically distributed the author proves a stong law of large numbers (SLLN) w.r.t. the so-called \(d_\infty\)-metric. As basic tool the representation theorem of fuzzy numbers by level sets is used (Goetschel & Voxman). Due to the long delay between acception of the paper (1997) and publication (2000) a comparison with other recently developed approaches to SLLN w.r.t. \(d_\infty\) is missing [e.g. A. Colubi, M. López-Díaz, J. Santos Domínguez-Menchero and M. Angeles Gil, Probab. Theory Relat. Fields 114, No. 3, 401-417 (1999; Zbl 0933.60023) and I. S. Molchanov, J. Math. Anal. Appl. 235, No. 1, 349-355 (1999; Zbl 0959.60003)].

MSC:

60F15 Strong limit theorems
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