Designing compact fuzzy rule-based systems with default hierarchies for linguistic approximation

This paper illustrates how a genetic algorithm can be employed for designing a compact fuzzy rule-based system, which linguistically describes a nonlinear function with many inputs in a human understandable manner. First we show that general fuzzy if-then rules with only a few antecedent conditions are necessary for such linguistic modeling when nonlinear functions have many input variables. Next we illustrate a new fuzzy reasoning method for handling fuzzy if-then rules with different specificity levels (i.e., for handling a mixture of general and specific fuzzy if-then rules). The fuzzy reasoning method is formulated based on the concept of default hierarchies of Holland et al.(1986) for calculating output values in a similar manner to human thinking. Then we formulate a rule selection problem for finding a small number of relevant fuzzy if-then rules among a large number of possible combinations of antecedent and consequent linguistic values. The rule selection problem has two objectives: to minimize the prediction error and to minimize the number of selected rules. A genetic algorithm is applied to the rule selection problem. Finally we suggest how genetics-based machine learning approaches (i.e., Pittsburgh and Michigan) can be used for linguistic modeling of nonlinear functions.