INTERPOLATION OF FUZZY IF-THEN RULES BY NEURAL NETWORKS

A number of approaches have been proposed for implementing fuzzy if-th en rules with trainable multilayer feedforward neural networks. In the se approaches, learning of neural networks is performed for fuzzy inpu ts and fuzzy; targets. Because the standard back-propagation (BP) algo rithm cannot be directly applied to fuzzy data, transformation of fuzz y data into non-fuzzy data or modification of the learning algorithm i s required. Therefore the approaches for implementing fuzzy if-then ru les can be classified into two main categories: introduction of prepro cessors of fuzzy data and modification of the learning algorithm. In t he first category, the standard BP algorithm can be employed after gen erating non-fuzzy data from fuzzy data by preprocessors. Two kinds of preprocessors based on membership values and level sets are examined i n this paper. In the second category, the standard BP algorithm is mod ified to directly handle the level sets (i.e., intervals) of fuzzy dat a. This paper examines the ability of each approach to interpolate spa rse fuzzy if-then rules. By computer simulations, high fitting ability of approaches in the first category and high interpolating ability of those in the second category are demonstrated.