On Nie-Tan Operator and Type-Reduction of Interval Type-2 Fuzzy Sets

Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this paper, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifying interval type-2 fuzzy sets.