Selection of rules by orthogonal transformations and genetic algorithms to improve the interpretability in fuzzy rule based systems

Fuzzy modeling is one of the best known techniques to model systems and processes. In most cases, as in data-driven fuzzy modeling, these fuzzy models reach a high accuracy, but show poor performance in complexity or interpretability, which are key aspects of Fuzzy Logic. There are several approaches in the literature to deal with the complexity and interpretability challenges for fuzzy rule based systems (FRBSs). In this paper, a post-processing approach is proposed via a genetic rule selection based on the relevance of each rule (using Orthogonal Transformations (OTs), in this case P-QR) and the well-known accuracy-interpretability trade-off. The main objective is to check the true significance, drawbacks and advantages of the rule selection based on OTs to manage the accuracy-interpretability trade-off. In order to achieve this aim, a neuro-fuzzy system (FasArtFuzzy Adaptive System ART based) and several case studies from the KEEL Project Repository are used to tune and check this selection of rules based on rule relevance by OTs, genetic selection and accuracy-interpretability trade-off. This neuro-fuzzy system generates Mamdani FRBSs, in an approximate way. SPEA2 is the multi-objective evolutionary algorithm (MOEA) tool used to tune the proposed rule selection, and different interpretability measures have been considered.