In a nonstatistical setting, a strong law of large numbers with respect to a set-valued probability measure was proved by M. C. Puri and D. A. Ralescu (1983). The author considers an extension of the results to situations where the measures are fuzzy set-valued. Probability values such as small, large, approximately 0.6, very large, and so on are part of the framework of fuzzy set-valued measures. The author defines the concepts of fuzzy probability measure and the expected value (integral) of a random vector in this framework. The main result is a strong law of large numbers with respect to a fuzzy probability measure. This framework is useful in Bayesian inference with a prior containing a mixture of probabilistic-fuzzy information.
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机译：在非统计环境中，M。C. Puri和D. A. Ralescu（1983）证明了关于定值概率测度的强大的大数定律。作者考虑将结果扩展到度量值是模糊集值的情况。诸如小，大，大约0.6，非常大等之类的概率值是模糊集值测度框架的一部分。作者在此框架中定义了模糊概率测度的概念和随机向量的期望值（积分）。主要结果是关于模糊概率测度的强大的大量定律。该框架在贝叶斯推断中有用，该先验包含概率模糊信息的混合。
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