Rule-based modeling: fast construction and optimal manipulation

This paper considers the problem of modeling an unknown system by a rule-based model constructed from measured data. In particular, we address two fundamental issues associated with the rule-based modeling: rule-base construction and rule-base manipulation. A two-step approach consisting of a principal and a refining algorithm has been suggested to extract rules from the available data set. Starting from the notion of product space clustering, we have developed three principal algorithms in which fuzzy concepts and competitive learning are utilized. A particular attention is paid to enabling the algorithms to have self-organizing capability and real-time applicability. Two algorithms have been presented for manipulating the obtained rule-base with novel data, one being a direct application of a fuzzy control algorithm and the other being an optimal algorithm in the sense of least square error with respect to an appropriately chosen cost function. Simulation results on three examples taken from function approximation, time-series prediction, and nonlinear dynamical modeling are given.