Limit theorems for fuzzy-random variables

This paper deals with limit theorems for fuzzy-valued measurable mappings which provide, as a whole, a foundation of statistical analysis with fuzzy data. A strong law of large numbers, a central limit theorem and a Gliwenko-Cantelli theorem are proved. The results are formulated simultaneously with respect to the L-p-metrics on the fuzzy sample spaces, investigated by Diamond and Kloeden. In particular, these versions of the limit theorems are related to identical, compatible concepts of convergence and measurability in the fuzzy sample spaces. The proofs of the theorems are based heavily on isomorphic isometric embeddings of the fuzzy sample spaces, endowed with L-p-metrics, into respective L-p-spaces, which are Banach spaces of type 2. These embeddings provide the application of convergence results in Banach spaces. (C) 2002 Elsevier Science B.V. All rights reserved.