ON A COMPUTATION OF HIGHER DEGREE FUZZY TRANSFORM COMPONENTS

The aim of this contribution is a general definition of the components of direct higher degree fuzzy transform. The original paper on the higher degree fuzzy transform deals with the bases of orthogonal polynomials that are computed by the Gram- Schmidt orthogonalization process with respect to the weights represented by basic functions of a given fuzzy partition. In some cases, the derivation of components can be very complex and imprecise, mainly, if the higher degrees of polynomials are considered. We propose a simple matrix algebra for matrices with real or complex-valued functions as their elements and show how the higher degree fuzzy transform components can be computed from an arbitrary basis.