Learning of Trapezoid Fuzzy Number Weights in Fuzzy Neural Networks

Abstract

This paper proposes a learning algorithm of fuzzy weights that are given as non-symmetric trapezoid fuzzy numbers in three-layer feedforward fuzzy neural networks. In the proposed learning algorithm, adjustment rules for the four parameters of each fuzzy weight are derived from a cost function defined for the level sets of fuzzy number outputs and fuzzy number targets. Since non-symmetric trapezoid fuzzy numbers include real numbers, intervals and triangular fuzzy numbers as special cases, the learning algorithm proposed in this paper can be viewed as a generalization of our former studies on fuzzy neural networks and interval neural networks. It is demonstrated by computer simulations that the ability of fuzzy neural networks to implement fuzzy if-then rules is drastically improved by such a generalization.