Multi - objective Evolutionary Membership Functions Tuning as a Post - processing Task in the Generation of Fuzzy Classification Systems

In multi-objective evolutionary fuzzy systems, the process of tuning the membership functions plays an important role towards optimizing the systems accuracy. Although, the shape and position of the membership functions in the partition should not change too much with relation to the original partition, so that it does not lose its integrity. This paper presents and discusses multi-objective evolutionary tuning of membership functions of fuzzy classification systems as a post-processing task, after the fuzzy rule base has been generated also by a multiobjective evolutionary process. The learning of the rule base uses the iterative approach and a fixed data base. The fitness evaluation considers two objectives. The first objective is based on the integrity and consistency of each rule, and the second one is defined as the number of conditions of each rule. The tuning of the membership functions also considers two objectives. The first objective is the accuracy of the rule base, calculated as the classification rate and the second objective is the interpretability of the fuzzy partitions, defined as a semantic based interpretability index proposed in the literature. The NSGA-II algorithm is used in both stages. The paper evaluates the results obtained in several datasets, comparing the ones generated with and without the membership functions tuning process. This comparison shows that the tuning method can improve the accuracy, without decreasing the semantic and complexity interpretability of the fuzzy rule based classifier. Keywords—Multi-objective evolutionary fuzzy systems; membership function tuning; NSGA-II; fuzzy rule-based classification systems