Optimal order of convergence for α-cut based fuzzy interpolators

This paper investigates the approximation behaviour of the α-cut based fuzzy interpolators. First, it is shown that the so-called KH fuzzy interpolator is a fuzzy generalization of a well-known and thoroughly investigated parameterized interpolatory operator from approximation theory, the Shepard operator. Exploiting the aforementioned relationship, we establish analog results on the approximation rate of KH controllers. The optimal order and class of approximation (saturation problem) are determined for certain values of the parameter λ. Corresponding results on the MACI method, being a modification of the KH interpolator, are also provided.