New aspects of interpretability of fuzzy systems for nonlinear modeling

Abstract

Fuzzy systems are well suited for nonlinear modeling. They can be effectively used if their structure and structure parameters are properly chosen. Moreover, it should be ensured that system rules are clear and interpretable. In this paper we propose a new algorithm for automatic learning and new interpretability criteria of fuzzy systems. Interpretability criteria are related to all aspects of those systems, not only their fuzzy sets and rules. Therefore, proposed criteria also concern parameterized triangular norms, discretization points and weights of importance from the rule base. As of the present time similar solutions have not been discussed in the literature. The proposed criteria are taken into account in the learning process, which is carried out with the use of a new learning algorithm. It was created by combining the genetic and the firework algorithms (this particular combination makes it possible to automatically choose not only system parameters but also its structure). It is an important advantage as most of the learning algorithms can only select system parameters when their structure has been specified by the designer. Proposed solutions were tested using typical simulation problems of nonlinear modeling.