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Probability of fuzzy events defined as denumerable additivity measure. (English) Zbl 0604.60005
In this paper the probability of fuzzy events is defined as a denumerable additivity measure. This definition is based on a non-conventional approach of separativity between fuzzy subsets. The presented measure fulfils all properties analogous to the properties of classical probability in the crisp case. Further, the notion of conditional probability of fuzzy events, complete fuzzy repartition and independent fuzzy events are defined by means of the probability measure considered here. Connections between all the above notions are presented in this paper, too. Finally, the Bayes formula is proved for the fuzzy case.

MSC:
60A99 Foundations of probability theory
03E72 Theory of fuzzy sets, etc.
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