The solution of Hutn\'ik's open problem

TL;DR

This paper solves an open problem in fuzzy set theory by proving that the only semicopula satisfying the specified conditions is the Łukasiewicz t-norm, thus providing a definitive answer to the posed question.

Contribution

It identifies the unique semicopula solution to Problem 9.2, clarifying the structure of solutions in fuzzy set theory.

Findings

The class of solutions contains only the Łukasiewicz t-norm.

Provides a definitive solution to an open problem in fuzzy set theory.

Clarifies the uniqueness of the semicopula in the problem context.

Abstract

In this note, we give a solution to Problem $9.2$, which was presented by Mesiar and Stup\v{n}anov\'a [{\it Open problems from the 12th International Conference on Fuzzy Set Theory and Its Applications}, Fuzzy Sets and Systems (2014), http://dx.doi.org/10.1016/ j.fss.2014.07.012]. We show that the class of semicopulas solving Problem $9.2$ contains only the {\L}ukasiewicz t-norm.