Effects of fine fuzzy partitions on the generalization ability of evolutionary multi-objective fuzzy rule-based classifiers

Evolutionary multiobjective optimization (EMO) algorithms have often been used to search for a number of non-dominated fuzzy rule-based classifiers with respect to their accuracy and complexity. It is, however, pointed out in some studies that the entire accuracy-complexity tradeoff surface is not always found by well-known and frequently-used EMO algorithms such as NSGA-II. Especially it is very difficult for EMO algorithms to find fuzzy rule-based classifiers with high accuracy around the edge of the tradeoff surface. One simple idea for the design of accurate fuzzy rule-based classifiers is the use of fine fuzzy partitions with a number of small antecedent fuzzy sets. The use of fine fuzzy partitions usually improves the accuracy of fuzzy rule-based classifiers on training data. It may, however, have some side-effects such as the deterioration of classification accuracy on test data and the increase in the search space for fuzzy system design. In this paper, we examine the use of fine fuzzy partitions in the evolutionary multiobjective design of fuzzy rule-based classifiers. Experimental results show that the use of fine fuzzy partitions almost always increases the number of obtained non-dominated fuzzy rule-based classifiers, almost always improve their training data accuracy, and often improve their test data accuracy for some data sets. We also examine the relation between the granularity of fuzzy partitions and the number of antecedent conditions (i.e., rule length).