GA-based approaches to linguistic modeling of nonlinear functions

We show two GA-based approaches to the linguistic modeling of nonlinear functions from numerical input-output data. Our task is to find a small number of linguistic rules for approximately realizing nonlinear functions. In both approaches, the fitness value of each rule set is defined by the weighted sum of three criteria: the total squared error, the number of linguistic rules, and their total length. The length of each rule is defined by the number of antecedent conditions. One approach is rule selection where a small number of linguistic rules are selected from a large number of candidate rules by genetic algorithms. The other approach is fuzzy genetics-based machine learning (GBML) where each linguistic rule is coded as a symbolic substring by its antecedent and consequent linguistic values. A rule set is represented by a concatenated string of variable length. The two approaches are compared with each other through computer simulations on numerical examples.