AN ARCHITECTURE OF NEURAL NETWORKS WITH INTERVAL WEIGHTS AND ITS APPLICATION TO FUZZY REGRESSION-ANALYSIS

In this paper, we first propose an architecture of neural networks that have interval weights and interval biases. A neural network with the proposed architecture maps an input vector of real numbers to an output interval. The target output is also given as an interval. Next we define a cost function using the interval output from the neural network and the corresponding target output. A learning algorithm is derived from the cost function in a similar manner as the BP (Back-Propagation) algorithm. We also show two variations of the learning algorithm for the proposed architecture, which lead to the inclusion relation between the interval output and the interval target. Last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers.