closeness; closeness matrix; closeness space; function similarity; fuzzy partition; fuzzy transform; preimage problem; singular value decomposition

In this talk, we present the paper "Preimage Problem Inspired by the F-Transform" that has been recently published. The authors (Jiří Janeček and Irina Perfilieva) proposed to establish a fuzzy partition of a given set of objects, such that closeness between these objects can be established as well. The goal is to describe the set of all functions mapped onto the same direct F-transform and thus to describe the similarity between discrete functions. Finding the former is called the preimage problem while the latter can be interpreted as finding the class of all functions that reconstruct the original one only based on its features with respect to the considered fuzzy-partitioned closeness space.