Possibility-function-based neural networks: case study of mathematical analysis
Li Chen, Donald H. Cooley, Jianping Zhang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
In this paper, we give a theoretical analysis for a generalized fuzzy neural network created in our previous papers. This analysis includes a mathematical proof of the training formulas used by such a network. the fuzzy neural network can accept a set of possibility functions as input as well as a vector of scalar values. This network consists of three components: a parameter-computing network, a converting layer, and a standard backpropagation-based neural network. The output vector of each layer of the parameter-computing network is a possibility vector, each element of which is a possibility function. The output vector of the converting layer is a fuzzy set, which represents the class membership values. In this paper only the first two components are considered.