Fuzzy and Fourier Transforms

Abstract

The fuzzy transform (F-transform for short) is a universal tool for a fuzzy modeling with convincing applications to image processing. The aim of this contribution is to explain the eect of the Ftransform in image processing. With this purpose, we investigate properties of the Fourier transform over the F-transform components. We prove that the direct F-transform is a low-pass filter. This explains specific tools and methodologies that are developed in the F-transform applications to the image processing.