Contents I. Introduction
Type-2 fuzzy sets (T2 FSs) generalize T1 FSs so that uncertainty associated with the membership function is taken into account [1]. Compared with a T1 FS, in which the membership is represented by crisp numbers, the membership of a T2 FS is represented by an FS, which is known as the secondary membership. Defuzzification is the final stage of a fuzzy inference system, in which an FS is converted into a crisp number. Unfortunately, defuzzification of a T2 FS can be so computationally complex that it has been known as the defuzzification bottleneck [2]. Defuzzification of T2 FSs usually contains two stages [3]: a type-reduction stage, in which the T2 FS is converted to a T1 FS, and a defuzzification of the T1 FS stage. It is the type-reduction stage that leads to the defuzzification bottleneck since there have been a number of efficient methods for the defuzzification of T1 FSs. One of the most popular methods to defuzzify T1 FSs is the centroid [4], [5] \begin{equation} d_c(\mu (x))=\frac{\int _{x_{\min }}^{x_{\max }} \mu (x)\cdot xdx}{\int _{x_{\min }}^{x_{\max }} \mu (x)dx} \end{equation}
