Abstract: Distance measures of fuzzy sets have been developed for feature selection and finding redundant features in the fields of decision-making, prediction, and classification problems. Terms commonly used in the definition of fuzzy sets are normal and convex fuzzy sets. This paper extends the general fuzzy set definitions to subnormal and non-convex fuzzy sets that are more precise when implementing uncertain knowledge representations by weighing fuzzy membership functions. A distance measure method for subnormal and non-convex fuzzy sets is proposed for embedded feature selection. Constructing fuzzy membership functions and extracting fuzzy rules play a critical role in fuzzy classification systems. The weighted fuzzy membership functions prevent the combinatorial explosion of fuzzy rules in multiple fuzzy rule-based systems. The proposed method was validated by a comparison with two other methods. Our proposed method demonstrated higher accuracies in training and test, with scores of 97.95% and 93.98%, respectively, compared to the other two methods.
