On S-homogeneity property of seminormed fuzzy integral: An answer to an open problem

We give an answer to Problem 9.3 stated by Mesiar and Stupňanová [8]. We show that the class of semicopulas solving this problem contains any associative semicopula S such that for each a ∈ [0, 1] the function x ↦ S(a, x) is continuous and increasing on a countable number of intervals.