Matrix Modeling of Hierarchical Fuzzy Systems

A matrix procedure to obtain a hierarchical decomposition of a multiple-input–single-output (MISO) fuzzy system is proposed. It is based on the fast inference using transition matrices (FITM) framework recently described. The resulting hierarchical system is totally equivalent to the original one in terms of input–output relation. A study of the rule-reduction capability of this system is carried out. Additionally, this paper describes a rule-base definition procedure of each of the systems resulting within the hierarchy. This procedure is based on closed-form analytical expressions and it does not need any manual interaction.