An ensemble of logical-type neuro-fuzzy systems

Neuro-fuzzy classifiers are characterized by incorporation of the expert knowledge into their construction. The most popular neuro-fuzzy systems are Mamdani-type systems. The main groups of neuro-fuzzy systems are also Takagi–Sugeno and logical-type systems. The latter were very rarely studied in the literature, however it was shown that logical-type reasoning transpired to be better suited for classification tasks whereas Mamdani-type reasoning for approximation problems (Rutkowska & Nowicki, 2000; Rutkowski & Cpałka, 2003, 2005). It is well known that an ensemble of several classifiers improves classification accuracy. Many ensembling methods are meta-learning techniques, thus they can be used to design ensembles of various member classifiers. paper an ensemble of logical-type neuro-fuzzy systems, based on S-implications, is proposed. The design of such an ensemble, and fuzzy ensemble in general, is a challenging task and encounters technical difficulties. The major problem is that such an ensemble contains separate rule bases which cannot be directly merged. As systems are separate, we cannot treat fuzzy rules coming from different systems as rules from the same (single) system. In the paper, the problem is addressed by a novel design of fuzzy systems constituting the ensemble, resulting in normalization of individual rule bases during learning. Several experiments illustrate the idea presented in the paper.