Multivariate fuzzy neural network interpolation operators and applications to image processing

Abstract

In this paper, we introduce a novel family of multivariate fuzzy neural network interpolation operators activated by sigmoidal functions belonging to the new class of multivariate sigmoidal functions. To present an alternative way to the well-known shortcomings of the Hukuhara difference, we use a proper function defined on a set of fuzzy n-cell numbers. Moreover, we construct the Kantorovich variant of fuzzy NN interpolation operators, and also achieve approximation properties via Lp-type metric with respect to both modulus of continuity and Lp-modulus of continuity in fuzzy sense. Various special examples for the class of multivariate sigmoidal functions are presented. Also, we give some illustrative examples to demonstrate the approximation performances of all the above operators. Finally, we give a novel interpolation algorithm involving a multidimensional fuzzy inference system with applications in color image resizing and inpainting.