Extension of Karnik-Mendel algorithms with uncertainty bound method

Karnik-Mendel (KM) algorithms are important tools in the type-2 fuzzy logic. They are commonly used in the centroid computation and type reduction of fuzzy sets and fuzzy systems. In the present paper, by combing KM algorithms and the uncertainty bound methods, new iterative algorithms which extend KM algorithms are proposed. The new algorithms get the lower bound and upper bound alternatively, which can be seen as the dynamic uncertainty bound methods and extensions of KM algorithms, where uncertainty bound can always obtained and updated from the iteration process. Numerical examples illustrate our proposed approach.