Checking orthogonal transformations and genetic algorithms for selection of fuzzy rules based on interpretability-accuracy concepts

Fuzzy modeling is one of the most known and used techniques in different areas to emulate the behavior of systems and processes. In most cases, as in data-driven fuzzy modeling, these fuzzy models reach a high performance from the point of view of accuracy, but from other points of view, such as complexity or interpretability, the models can present a poor performance. Several approaches are found in the specialized literature to reduce the complexity and improve the interpretability of the fuzzy models. Here, a post-processing approach is taken into account via the definition of the rules selection criterion that aims to choose the most relevant rules according to the well-known accuracy-interpretability trade-off. This criterion is based on Orthogonal Transformations, here the QRP transformation is taking into consideration, and its parameters are tuned genetically. The main objective is to check the true significance, drawbacks and advantages the firing matrix of the rules, that is the foundation of the most usual approaches based on orthogonal transformations for the complexity reduction of the fuzzy models. A neuro-fuzzy system, FasArt (Fuzzy Adaptive System ART based), and several case studies, data sets from the KEEL Project Repository, are used to tune and check this approach. This neuro-fuzzy system generates Mamdani fuzzy rule based systems (FRBSs), each with its own particularities and complexities from the point of view of fuzzy sets and rule generation. NSGA-II is the MOEA tool used to tune the criterion parameters based on accuracy-interpretability ideas.