Genetic-algorithm-based approach to linguistic approximation of nonlinear functions with many input variables

We propose a genetic-algorithm-based approach for extracting a small number of fuzzy if-then rules with clear linguistic meanings from numerical input-output data. The goal is to construct a comprehensible fuzzy rule-based system from numerical input-output data. The comprehensibility of a fuzzy rule-based system is evaluated by three criteria: linguistic interpretability of fuzzy if-then rules; simplicity of fuzzy if-then rules; and compactness of a fuzzy rule-based system. We first illustrate the necessity of general rules with many "don't care" conditions when we try to construct compact fuzzy rule-based systems for high-dimensional problems without the exponential increase in the number of fuzzy if-then rules. Then we illustrate a fuzzy reasoning method for realizing default hierarchies of fuzzy if-then rules. Finally, we show how genetic algorithms can be utilized for generating a small number of fuzzy if-then rules from numerical input-output data.