Multiobjective genetic fuzzy systems

Abstract

This chapter explains evolutionary multiobjective design of fuzzy rule-based systems in comparison with single-objective design. Evolutionary algorithms have been used in many studies on fuzzy system design for rule generation, rule selection, input selection, fuzzy partition, and membership function tuning. Those studies are referred to as genetic fuzzy systems because genetic algorithms have been mainly used as evolutionary algorithms. In many studies on genetic fuzzy systems, the accuracy of fuzzy rule-based systems is maximized. However, accuracy maximization often leads to the deterioration in the interpretability of fuzzy rule-based systems due to the increase in their complexity. Thus, multiobjective genetic algorithms were used in some studies to maximize not only the accuracy of fuzzy rule-based systems but also their interpretability. Those studies, which can be viewed as a subset of genetic fuzzy system studies, are referred to as multiobjective genetic fuzzy systems (MoGFS). A number of fuzzy rule-based systems with different complexities are obtained along the interpretability-accuracy tradeoff curve. One extreme of the tradeoff curve is a simple highly interpretable fuzzy rule-based system with low accuracy while the other extreme is a complicated highly accurate one with low interpretability. In MoGFS, multiple accuracy measures such as a true positive rate and a true negative rate can be simultaneously used as separate objectives. Multiple interpretability measures can also be simultaneously used in MoGFS.