A wrapper methodology to learn interval-valued fuzzy rule-based classification systems
José Sanz, Humberto Bustince
Abstract
Learning an interval-valued fuzzy rule-based classification system is a challenge as its success directly depends on the interval-valued fuzzy partition used. In fact, the learning of an interval-valued fuzzy system usually starts by creating a partition composed of numerical fuzzy sets, which are used to build an initial fuzzy classifier. Then, it is augmented with interval-valued fuzzy sets whose shape is subsequently optimized to improve the system’s performance. However, as in this methodology the fuzzy rules are learned using numerical fuzzy sets, the benefits of the interval-valued fuzzy sets may not be fully exploited. In this paper we define a new learning methodology that avoids building the initial fuzzy classifier but directly learns interval-valued fuzzy rules. To do so, we define a wrapper methodology to learn the interval-valued fuzzy partitions such that they lead to an interval-valued fuzzy rule-based classification system as accurate as possible. Moreover, our new method allows one to represent each membership function using the most proper type of fuzzy set for the sake of modeling the uncertainty in the best possible manner. Consequently, the antecedents of the rules can be formed of only numerical fuzzy sets, only interval-valued fuzzy sets or a mixture of both. The quality of the proposal is compared versus four state-of-the-art fuzzy classifiers like FARC-HD, IVTURS, FURIA and FARC-HD using an inference based on a generalization of the Choquet integral. We also compare our new approach besides its numerical fuzzy counterpart to clearly show the benefits of the usage of interval-valued fuzzy sets. Specifically, the average accuracy rate of our new method is 81.17%, which is at least 0.66% better than the remainder state-of-the-art fuzzy classifiers.