A Fast and Accurate Method for Calculating the Center of Gravity of Polygonal Interval Type-2 Fuzzy Sets

Defuzzification plays an important role in the applications of interval type-2 fuzzy sets (IT2FSs). However, computational complexity of existing defuzzification methods has turned this procedure into an important bottleneck toward the use of IT2FSs. It has been proved that the Nie-Tan method is an accurate discretizing-based method for calculating the center of gravity (COG) of IT2FSs. In this article, we propose a fast and accurate method for calculating the COG-Nie-Tan defuzzification-of polygonal IT2FSs on discrete and continuous domains without the need of discretization. The proposed method calculates the accurate COG for trapezoidal and triangular IT2FSs as special cases of polygonal IT2FSs. Moreover, any IT2FS can be approximated by a polygonal IT2FS-the higher the order of polygonal IT2FS, the better the approximation. Hence, using the proposed method on an IT2FS that is approximated by an appropriate polygonal IT2FS results in a more accurate COG.