Centroid type-reduction of interval type-2 fuzzy logic systems based on extended binary algorithms

In the application of interval type-2 (IT2) Mamdani fuzzy logic systems (FLSs), centroid type-reduction is a commonly used reduction method. This paper introduces two new algorithms, the Binary algorithm and its extended version, the Extended-Binary algorithm, to address the centroid reduction problem in IT2 Mamdani systems. These two algorithms are compared with the EKM algorithm, with a focus on comparing their accuracy and computational efficiency when calculating defuzzification values based on the continuous Nie-Tan (CNT) method. Four simulation experiments are conducted to test the Extended-Binary algorithm, the Binary algorithm, and the EKM algorithm. The results show that the Extended-Binary algorithm outperforms both the Binary algorithm and the EKM algorithm in terms of accuracy and computational efficiency.