Fuzzy Functions, Relations, and Fuzzy Transforms (2012)

Fuzzy groups, fuzzy functions and fuzzy equivalence relations

To each fuzzy subgroup a fuzzy equivalence relation is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation. In the de-nition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp. In an opposite direction, another structure can be constructed maintaining c...

Approximation of Fuzzy Functions by Extended Fuzzy Transforms

A fuzzy approximation method called fuzzy transforms for approximation of continuous function is presented in this paper. It is shown how can be fuzzy transforms naturally generalized for functions with more variables. A fuzzy function as an approximated mapping is considered. This leads to an extension of fuzzy transforms for fuzzy function as well as to an extension of generalized fuzzy trans...

Fuzzy and Fourier Transforms

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 effect of the F transform 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. Thi...

Fuzzy Partial Order Relations and Fuzzy Lattices

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its l...

Fuzzy transforms and universal approximation