On homogeneity of the smallest semicopula-based universal integral in the class of pseudo-continuous semicopulas

Abstract

In this paper, we introduce the concept of pseudo-continuous semicopula. We show its relationship with continuity in the second variable and provide a characterization of all semicopulas S such that the smallest semicopula-based universal integral is S-homogeneous. This completely solves Open problem 2.29 proposed by J. Borzová-Molnárová et al. in the paper [2].