Fuzzy arithmetic in neural networks for linguistic rule extraction

We have already proposed a fuzzy arithmetic-based method for extracting linguistic if-then rules from trained neural networks for pattern classification problems with continuous attributes. In our method, antecedent linguistic values of a linguistic if-then rule are presented to a trained neural network as inputs, and the corresponding fuzzy outputs are calculated by fuzzy arithmetic. The consequent class and the grade of certainty are determined based on the calculated fuzzy outputs. Thus the calculation of the fuzzy outputs is very important for the linguistic rule extraction. Because the fuzzy arithmetic is locally applied to the calculation at each unit, the fuzziness of the linguistic input values is usually increased by the feedforward calculation through the neural network. In this paper, we show how such increase of the fuzziness can be reduced by subdividing the level set (i.e., alpha - cut) of each linguistic input value in the calculation of the fuzzy outputs. The effect of such subdivision is illustrated by computer simulations.