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Optimising the Fuzzy Granulation of Attribute Domains

The definitions of the number of fuzzy sets and their proper distribution on their domains are fundamental issues for fuzzy systems since these basic parameters deeply affect the quality of the systems results, both in terms of performance rates and interpretabil- ity. Several methods have been proposed in the literature to define these parameters, although it is common to find works in which the number of fuzzy sets is defined empirically, distributing them equally in the domains. This paper presents a fast and easy method to esti- mate the number of fuzzy sets for each attribute and compares three methods for the distribution of fuzzy sets. Two of them are non- supervised methods, using same width and same frequency, the third one is an adaptation of the 1-R supervised method to discretize at- tributes. Experiments with 10 datasets for classification problems, 10-fold cross validation, using the Wang & Mendel method, and the classic and general fuzzy reasoning methods are presented and dis- cussed.