Fast and accurate center of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions

Abstract

In this article three methods are presented to perform the center of gravity (COG) defuzzification method in the context of linguistic fuzzy models with t-norm-based inference: one well-known method, the discretisation method, and two new methods, the slope-based method and the modified transformation function method. The methods are worked out for trapezoidal membership functions forming a fuzzy partition in the sense of Ruspini. Experimental results show that the newly introduced methods exhibit excellent accuracy at an extremely low computational cost compared to the widely applied discretisation method.