Chance measure for hybrid events with fuzziness and randomness |
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Authors: | Xiang Li Baoding Liu |
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Affiliation: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China |
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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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Keywords: | Fuzzy variable Hybrid variable Chance measure Expected value Entropy |
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