Construction of weak homogeneity from interval homogeneity. Application to image segmentation

In this paper we axiomatically define weak homogeneity of a fuzzy subset, which means that its membership function fulfills at least the minimum properties required to represent the homogeneity of a region. We also provide several construction methods based on the homogeneity of an interval. Besides, we show an illustrative example of these functions applied to the problem of image segmentation.