Incremental smooth support vector regression for Takagi–Sugeno fuzzy modeling

We propose an architecture for Takagi–Sugeno (TS) fuzzy system and develop an incremental smooth support vector regression (ISSVR) algorithm to build the TS fuzzy system. ISSVR is based on the εε-insensitive smooth support vector regression (εε-SSVR), a smoothing strategy for solving εε-SVR, and incremental reduced support vector machine (RSVM). The ISSVR incrementally selects representative samples from the given dataset as support vectors. We show that TS fuzzy modeling is equivalent to the ISSVR problem under certain assumptions. A TS fuzzy system can be generated from the given training data based on the ISSVR learning with each fuzzy rule given by a support vector. Compared with other fuzzy modeling methods, more forms of membership functions can be used in our model, and the number of fuzzy rules of our model is much smaller. The performance of our model is illustrated by extensive experiments and comparisons.