Basic properties of the interval-valued fuzzy morphological operators

Mathematical morphology is a theory to extract specific information such as edges and patterns from images. The original binary morphology, for binary black and white images, was extended to greyscale images, amongst others, by a fuzzy approach known as fuzzy mathematical morphology. This approach was based on the observation that greyscale images and fuzzy sets can be modelled in the same way. Recently, fuzzy mathematical morphology has been further extended based on extensions of classical fuzzy set theory. In this paper, we focus on the extension based on interval-valued fuzzy set theory, i.e., interval-valued fuzzy morphology, and we give an overview of the basic properties that hold in this model.