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Towards a theory of fuzzy probability for cognitive computing

A theory of fuzzy probability is presented based on fuzzy sets, which extends the conventional evenly distributed probability space to a complex distribution of fuzzy probability space. A mathematical model of fuzzy probability is formally introduced in the fuzzy sample space. Algebraic operators of fuzzy probability are rigorously described with a set of theorems on the algebra of fuzzy probabilities. Typical applications of the fuzzy probability theory are illustrated for dealing with random fuzzy events, fuzzy causations, and semantic uncertainties in formal inference, qualification, quantification, classification, cognitive linguistics, cognitive informatics, computational intelligence, and cognitive computing.