A convergent smoothing algorithm for training max –min fuzzy neural networks

Abstract

In this paper, a smooth function is constructed to approximate the nonsmooth output of max –min fuzzy neural networks (FNNs) and its approximation is also presented. In place of the output of max –min FNNs by its smoothing approximation function, the error function, defining the discrepancy between the actual outputs and desired outputs of max –min FNNs, becomes a continuously differentiable function. Then, a smoothing gradient decent-based algorithm with Armijo–Goldstein step size rule is formulated to train max –min FNNs. Based on the existing convergent result, the convergence of our proposed algorithm can easily be obtained. Furthermore, the proposed algorithm also provides a feasible procedure to solve fuzzy relational equations with max –min composition. Finally, some numerical examples are implemented to support our results and demonstrate that the proposed smoothing algorithm has better learning performance than other two gradient decent-based algorithms.