Choice of effective fitness functions for genetic algorithm-aided dynamic fuzzy rule interpolation

Abstract

Fuzzy rule interpolation (FRI) has been a vital reasoning tool for sparse fuzzy rule-based systems. Throughout interpolative reasoning, an FRI system may produce a large number of interpolated rules, which generally serve no further purpose once the required outcomes have been obtained. However, this abandoned pool of interpolated rules can be used to improve the existing sparse rule base, because they contain useful information on the underlying problem domain. Efficient extraction of knowledge from such a pool of interpolated rules are indeed helpful to analyse and update the sparse rule base, leading to a dynamic sparse fuzzy rule base for building an enhanced fuzzy system. Following this idea, a genetic algorithm (GA) based dynamic fuzzy rule interpolation framework has been proposed recently. This paper presents an extension of the dynamic FRI system. In particular, it investigates different fitness functions and their effects on the outcomes of the GA-based system. A variety of fitness functions based on cluster quality indices are employed and tested, including Dunn Index, Davies-Boulding Index, Ball-Hall Index and BetaCV Index. Experimental investigation demonstrates that results obtained by the use of Dunn index or Davies-Bouldin index are better than those by Ball-Hall or BetaCV index, with those using Davies-Bouldin index performing the best overall. Such results offer an empirical guideline for the selection of the fitness function in implementing accurate GA-based dynamic FRI systems.