A reduction approach for fuzzy rule bases of fuzzy controllers

In this paper, a new approach to reducing the number of rules in a given fuzzy rule base of a fuzzy controller is presented. The fuzzy mechanism of the fuzzy controller under consideration consists of the product-sum inference, singleton output consequents and centroid defuzzification. The output consequents in the cells of the rule table are collected and represented as an output consequent matrix. The feature of the output consequent matrix is extracted by the singular values of the matrix. The output consequent matrix is reasonably approximated with a dominant consequent matrix. Also, the elements of the dominant consequent matrix is determined to minimize the approximation error function. Then the size of the dominant consequent matrix (the size of the fuzzy rule base) is reduced through the rule combination approach. The scaling factors for the fuzzy controller with the reduced rule table are adjusted to have the control system satisfy the performance indices. The effectiveness of the proposed approach is shown using simulation and experimental results.