An Extension of the FuzzyR Toolbox for Non-Singleton Fuzzy Logic Systems

Abstract

Recent years have seen a surge in interest in non-singleton fuzzy systems. These systems enable the direct modelling of uncertainty affecting systems' inputs using the fuzzification stage. Moreover, recent work has shown how different composition approaches to modelling the interaction between the non-singleton input and the antecedent fuzzy sets enable the efficient handling of uncertainty without requiring changes in a system's rule base, with benefits both in terms of performance and interpretability. As thus far few current software toolkit support non-singleton fuzzy systems, this paper presents an extension of the FuzzyR toolbox, which is a freely available R package on CRAN, for non-singleton fuzzy logic systems. The updated toolbox enables a non-singleton model to be conveniently built from scratch, or for existing singleton fuzzy logic systems built using FuzzyR to be converted easily. Predefined operations include fuzzification of crisp inputs (e.g. into Gaussian membership functions), and a variety of composition approaches for computing rules' firing-strengths, based on the standard, centroid-based, and similarity-based methods. It is also possible to include user-defined options for these abovementioned methods, without the need to modify (or update) the FuzzyR toolbox itself. In this paper, detailed introductions for the new non-singleton features of the toolkit are presented, complete with code samples in R to facilitate adoption both within and beyond the community. Further, the paper presents a series of validation experiments, replicating a recent empirical analysis of non-singleton fuzzy logic systems in the context of time-series prediction with different levels of noise.