Probability theory in fuzzy sample spaces

Volker Krätschmer ()

Metrika: International Journal for Theoretical and Applied Statistics, 2004, vol. 60, issue 2, 167-189

Abstract: 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 2004

Keywords: Vagueness 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 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:60:y:2004:i:2:p:167-189

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DOI: 10.1007/s001840300303

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