Multipopulation Nature-Inspired Algorithm (MNIA) for the Designing of Interpretable Fuzzy Systems

The solutions proposed in this article are based on our experience with fuzzy systems (FSs), their interpretability, and population-based algorithms (PBAs). They provide a consistent approach to the design of interpretable FSs. First, PBAs can make a useful tool for selecting both parameters and the FS structure. In practice, such structure is usually chosen by trial and error. Second, in this article, we propose a new multipopulation PBA, which uses a variety of search formulas. This helps to eliminate the problem of incorrect PBA selection. Third, we propose interesting solutions for the interpretability of FSs with trapezoidal membership functions. These functions are well suited for modeling ranges of linguistic variables. We are particularly interested in providing them with original interpretability criteria, which are used by a PBA to design FSs. Furthermore, we offer an original way of setting up trapezoidal functions, which prevents them from overlapping with each other. Fourth, we believe that interpretability can be achieved through a capable extension of fuzzy rules. That is the reason why we used weights and dedicated operators for their processing. In this article, a different extension of the rules base is proposed. It involves adding relation operators (ROs) (e.g., “>” and “>=”), which can be used to model linguistic phrases, e.g. “electrical voltage less than or equal to high.” An additional task of the PBA is the automatic selection of an RO, which facilitates the extraction of knowledge from the data. The approach proposed in this article was tested using well-known classification benchmarks.