Fuzzy rule base reduction via singular value decomposition

This paper deals with a fuzzy rule base reduction via Singular Value Decomposition (SVD). The method consists of forming a rule consequents matrix, applying SVD procedure and then keeping only the larger singular values. Hence, the dimension of the reduced rule base depends on the number of the retained singular values. New membership functions are obtained by generating linear combinations of the original ones. This approach is applicable regardless of the input variable's number, the inference paradigm and the shape of the initial membership functions. In this work, the SVD reduction is applied in the case of rule base where all fuzzy rules are defined and the case of rule set including some missing rules. Fuzzy Logic Controllers (FLCs) exploiting these rule bases are considered to control an inverted pendulum.