Sparse data in the evolutionary generation of fuzzy models

Abstract

Fuzzy rule bases have proven to be an effective tool for modeling complex systems and approximating functions. Two approaches, global and local rule generation, have been identified for the evolutionary generation of fuzzy models. In the global approach, the standard method of employing evolutionary techniques in fuzzy rule base generation, the fitness evaluation of a rule base aggregates the performance of the model over the entire space into a single value. A local fitness assessment utilizes the limited scope of a fuzzy rule to evaluate the performance in regions of the input space. Regardless of the method employed, the ability to construct models is inhibited when training data are sparse. In this research, a multi-criteria fitness function is introduced to incorporate a bias towards smoothness into the evolutionary selection process. Several multi-criteria fitness functions, which differ in the extent of the assessment smoothness and the range of its application, are examined. A set of experiments has been performed to demonstrate the effectiveness of the multi-criteria strategies for the evolutionary generation of fuzzy models with sparse data.