Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of [InlineMediaObject not available: see fulltext.] The investigations are focussed on the discussion how to equip those sample spaces with suitable σ-algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature. Copyright Springer-Verlag 2004Vagueness of measurement, [InlineMediaObject not available: see fulltext.]spaces of fuzzy subsets, L p -metrics, random fuzzy sets, Aumann-expected value of random fuzzy sets, Glivenko-Cantelli theorem for random fuzzy sets, strong law of large numbers for random fuzzy sets, central limit theorem for random fuzzy sets,