PROBABILISTIC SETS IN IDENTIFICATION OF FUZZY SYSTEMS.

The paper deals with the theoretical problems of probabilistic sets treated as a means for expressing the ambiguity and randomness and its application in system analysis, especially identification and design of a fuzzy logic controller. The notion of a probabilistic set is based on both probability theory and fuzzy set theory defined by a pointwise measurable function from a parameter space (probability space) to a characteristic space (measurable space). The moment analysis especially convenient for practical purposes is considered. It is shown how probabilistic sets could be a proper tool for identification of fuzzy systems described by fuzzy relational equation (e. g. max-min equation). We discuss an important problem of generation of a matrix of a fuzzy logic controller when a collection of control rules X//i yields U//i (i equals 1, 2,. . . , N) is given. Because of competitive criteria of each rule, a clustering algorithm is applied and the proper form of implication operator is introduced.