Uncertainty modeling through probabilistic fuzzy systems

A novel concept of probabilistic fuzzy system (PFS) has been first proposed and a general framework for its representation has been developed here. Unlike the well established concept of fuzzy probability, which incorporates fuzziness in probabilities, PFS uses a new concept of probabilistic fuzzy rule to include randomness in fuzzy systems and hence are suitable for modeling real world systems which have both types of statistical and nonstatistical uncertainties. Using a multiple model approach, both continuous and discrete stochastically uncertain systems have been introduced as new concepts and it is shown how a probabilistic fuzzy system can be regarded as a discrete stochastically uncertain system (DSU). The problem of learning the parameters of a DSU has been next studied and simulation results show the behavior of a sample probabilistic fuzzy system