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Probability theory in fuzzy sample spaces

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  • Volker Krätschmer

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

Suggested Citation

  • Volker Krätschmer, 2004. "Probability theory in fuzzy sample spaces," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 167-189, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:167-189
    DOI: 10.1007/s001840300303
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    Cited by:

    1. Gil, Maria Angeles & Montenegro, Manuel & Gonzalez-Rodriguez, Gil & Colubi, Ana & Rosa Casals, Maria, 2006. "Bootstrap approach to the multi-sample test of means with imprecise data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 148-162, November.

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