Uninorms and Absorbing Norms in Image Processing

Recently it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. So, in Image Processing the sum and multiplication are not the only operations that can be used, but also, several other operations provided by fuzzy logic. In this sense, in the present paper, we will investigate how a pair consisting of a uninorm and an absorbing norm can be used for approximation purposes. We propose an approximation operator based on a continuous strictly increasing additive generator for the uninorm and on the same function used as a multiplicative generator for the absorbing norm. The proposed operator is defined based on the classical Shepard operator. We show that in Image Processing, the result of the proposed method outperforms in several cases the classical Shepard approximation operators based on sum and product operations.