An Incremental Approach to TS Fuzzy Modeling

This paper proposes an incremental smooth support vector regression (ISSVR) method for TS fuzzy modeling. Under certain assumptions on membership functions, we propose an optimization problem for TS fuzzy modeling based on the structural risk minimization principle. We show that this problem is an SVR problem with non-positive definite kernels. It cannot be solved using conventional SVR. Then we establish a connection between this TS fuzzy modeling problem and smooth support vector regression (SSVR), which is a smoothing strategy for solving SVR. The problem is always solvable using SSVR because SSVR puts no restrictions on the kernel. Then we apply an incremental approach to the SSVR by selecting informative samples from the training dataset. Taking advantage of SSVR, more forms of membership functions can be used in our model compared with conventional methods. Experiments show that the proposed ISSVR-based TS fuzzy model has good generalization ability with small number of fuzzy rules.