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Integrals of random fuzzy sets

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Abstract

This paper tries to give a systematic investigation of integration of random fuzzy sets. Besides the widely used Aumann-integral adaptions of Pettis- and Bochner-integration for random elements in Banach spaces are introduced. The mutual relationships of these competing concepts will be explored comprehensively, completing and improving former results from literature. As a by product dominated convergence theorems, strong laws of large numbers and central limit theorems for random fuzzy sets can be derived. They are based on weaker assumptions than previous versions from literature.

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  1. Statistics and Econometrics, Faculty of Law and Economics, University of Saarland, Germany

    Volker Krätschmer

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  1. Volker Krätschmer
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Correspondence to Volker Krätschmer.

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Krätschmer, V. Integrals of random fuzzy sets. Test 15, 433–469 (2006). https://doi.org/10.1007/BF02607061

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