Hypertrapezoidal fuzzy membership functions

The authors present a method for representing N-dimensional fuzzy membership functions. The proposed method is a generalization of the one-dimensional trapezoidal membership function commonly used in fuzzy systems. The issue of correlation between input variables and a decrease in the rule base size is the motivation for extending the definition of membership functions into more than one domain. The approach outlined in this paper is focused by practical considerations and use of a Bayesian version of fuzzy logic which requires that set membership sum to one. The fuzzy partitioning which stems from the presented method is parameterized by M+1 values, yielding an efficient mechanism for designing complex fuzzy systems