On the estimation of the number of fuzzy sets for fuzzy rule-based classification systems

Defining the attributes in terms of fuzzy sets is an essential part in designing a fuzzy system. The main tasks involved in defining the fuzzy data base include deciding the type of fuzzy set (triangular, trapezoidal, etc), the number of fuzzy sets for each attribute, and their distribution in each attribute domain. In the absence of an expert, these definitions can be done empirically or by using automatic methods. In this paper, we present four different methods to estimate the number of fuzzy sets for a dataset. The first defines the same number of fuzzy sets for all attributes, while the other three flexibly estimate different numbers of fuzzy sets for each attribute of a given dataset. The aim of this paper is to provide fast and practicable methods to define fuzzy data bases, previously to the generation of the fuzzy rule base by more costly approaches, such as genetic fuzzy systems. These methods are evaluated using the FuzzyDT method, which generates a fuzzy decision tree based on the C4.5 classic method, on 11 datasets. The results are compared in terms of accuracy and number of generated rules. The results showed that the flexible estimation of the number of fuzzy sets obtained better error rates for the datasets used in the experiments.