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When fuzzy measures are upper envelopes of probability measures

✍ Scribed by Volker Krätschmer

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 276 KB
Volume: 138
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(02)00463-3

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✦ Synopsis

Fuzzy measures which are upper envelopes of probability measures may play an important role to develop a general theory of Bayesian statistics. Especially from a technical point of view, a widely accepted generalized Bayes rule would be applicable for those kind of fuzzy measures.

We give su cient general conditions to ensure that fuzzy measures are upper envelopes of probability measures. They are applied to some special classes of important types of fuzzy measures, namely Sugeno fuzzy, plausibility and possibility measures. The proof of the main result is based on recently systemized inner extension procedures within abstract measure theory.

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