Generating fuzzy if-then rules from trained neural networks: linguistic analysis of neural networks

We propose a fuzzy-arithmetic-based approach for extracting fuzzy if-then rules from multilayer feedforward neural networks. For pattern classification problems, our approach extracts fuzzy if-then rules such as "If x/sub 1/ is small and x/sub 2/ is large then Class 1 with CF=0.9" where CF is the grade of certainty. In order to determine the consequent class and the grade of certainty of a fuzzy if-then rule, first an input vector of linguistic values is presented to a trained neural network. The input vector consists of linguistic values in the antecedent part of the fuzzy if-then rule (e.g. (small, large) in the case of the above fuzzy if-then rule). Next fuzzy outputs from the neural network are calculated by fuzzy arithmetic. Then the consequent class and the grade of certainty of the fuzzy if-then rule are determined by an inequality relation between the fuzzy outputs.