A new annealing robust fuzzy basis function for modeling with outliers

In this paper, the annealing robust fuzzy basis function (ARFBF) is proposed to improve the problems of the fuzzy basis function for modeling with outliers. Firstly, the repeated support vector regression (RSVR) approach is proposed to determine the initial structure of ARFBF in this paper. Because of a RSVR approach is equivalent to solving twice linear constrained quadratic programming problem under a fixed structure of SVR, the number of hidden nodes, initial parameters and initial weights of the ARFBF are easily obtained in the second SVR. Secondly, the results of RSVR are used as initial structure in ARFBF. At the same time, an annealing robust learning algorithm (ARLA) is used as the learning algorithm for ARFBF. That is, an ARLA is proposed to overcome the problems of initialization and the cut-off points in the robust learning algorithm. Hence, when an initial structure of ARFBF is determined by a RSVR approach, the ARFBF with ARLA have fast convergence speed and robust against outliers. Simulation results are provided to show the validity and applicability of the proposed ARFBF.