A Neural Network with Interval Weights and Its Application to Fuzzy Regression Analysis

Abstract

This paper proposes a new architecture of neural networks and derives its learning algorithms. The neural network with the proposed architecture has interval weights and interval biases. A cost function is defined using the interval output from the neural network and the corresponding target interval. A learning algorithm is derived from the cost function in a similar manner as the back-propagation algorithm. Two variations of the learning algorithm are also derived based on the inclusion relation between the interval output and the target interval. A method of fuzzification is shown to apply the neural network to the fuzzy regression analysis.