Three new uncertainty bound methods of Karnik-Mendel algorithms

Karnik-Mendel (KM) algorithms are important tools for the centroid computation or type reduction in the type-2 fuzzy logic. To release the possible computational bottleneck of the iteration of KM algorithms, some uncertainty bound methods are proposed. In the present paper, the current uncertainty bounds are extended and improved with three new uncertainty bound methods for the centroid computation of interval type-2 fuzzy sets. The New uncertainty bound methods can be further improved if some prior information is available or be be improved from the current bound values. Theoretical analysis proves the validity of our new approaches.