An answer to an open problem on seminormed fuzzy integral

TL;DR

This paper addresses an open problem in the theory of seminormed fuzzy integrals by characterizing a class of associative semicopulas with specific continuity and monotonicity properties.

Contribution

It provides a solution to Problem 9.3 from Mesiar and Stupnanova (2015), identifying a broad class of semicopulas satisfying certain conditions.

Findings

Class of semicopulas includes any associative semicopula with continuous and increasing slices on countable intervals.

Characterizes solutions to an open problem in fuzzy integral theory.

Advances understanding of the structure of semicopulas in fuzzy integrals.

Abstract

We give an answer to Problem 9.3 stated by by Mesiar and Stupnanova (2015). We show that the class of semicopulas solving this problem contains any associative semicopula S such that a the function S(a,.) is continuous and increasing on a countable number of intervals.