Compact TS-fuzzy models through clustering and OLS plus FIS model reduction

Identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy models of the Takagi-Sugeno (TS) type may be a good choice to describe such systems; however, in many cases these become soon complex. We propose a three-step method to obtain compact TS-models that can be effectively used to represent complex systems: 1) a new fuzzy clustering method is proposed for identification of compact TS-models; 2) the most relevant consequent variables of the TS-model are selected by an orthogonal least squares (OLS) method based on the obtained clusters; and 3) for selection of relevant antecedent variables, a new method is proposed based on Fisher's interclass separability (FIS) criterion. The overall approach is demonstrated by means of the MPG (miles per gallon) nonlinear regression benchmark. Results are compared with those obtained by standard linear, neuro-fuzzy and advanced fuzzy clustering-based identification tools.