Linguistic Modelling for Function Approximation Using Grid Partitions

Hisao Ishibuchi, Takashi Yamamoto, Tomoharu Nakashima

Abstract: Discusses various issues related to linguistic modeling of nonlinear functions with many input variables. Our task is to extract a small number of comprehensible linguistic rules from numerical data for describing nonlinear functions in a human understandable manner. First we show the necessity of general rules in the handling of nonlinear functions with many input variables. Next we compare a standard interpolation-based fuzzy reasoning method with our non-standard specificity-based method. When a rule base is a mixture of general and specific rules, different results are obtained from these two methods. Then we extend two performance measures (i.e., confidence and support) of association rules in data mining to the case of linguistic rules. These two measures are used for evaluating each linguistic rule. The validity of our fuzzy reasoning method is discussed using these measures. Finally we show two genetic algorithm-based approaches to linguistic modeling. One is a rule selection method, and the other is a genetics-based machine learning algorithm.