A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set

This article presents a recursive algorithm to compute the generalized centroid of an interval type-2 fuzzy set. First, a re-expression of the upper and lower limits of the generalized centroid is introduced. Then, the re-expressed formulas are solved by using a mixed approach of exhaustive search and recursive computations. This method is compared with the Karnik-Mendel iterative algorithm under the same computational principles. Experimental evidence shows that the recursive approach is computationally faster than the Karnik-Mendel method without loosing numeric precision.