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Chance measure for hybrid events with fuzziness and randomness

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Abstract

In many cases, fuzziness and randomness simultaneously appear in a system. Hybrid variable is a tool to describe this phenomena. Fuzzy random variable and random fuzzy variable are instances of hybrid variable. In order to measure hybrid event, a concept of chance measure is proposed in this paper. Furthermore, several useful properties about this measure are proved such as self-duality, subadditivity and semicontinuity. Some concepts are also presented such as chance distribution, expected value, variance, moments, critical values, entropy, distance and sequence convergences.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Xiang Li & Baoding Liu

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  1. Xiang Li
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  2. Baoding Liu
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Correspondence to Baoding Liu.

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Li, X., Liu, B. Chance measure for hybrid events with fuzziness and randomness. Soft Comput 13, 105–115 (2009). https://doi.org/10.1007/s00500-008-0308-x

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  • DOI: https://doi.org/10.1007/s00500-008-0308-x

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