Generalization of two-dimensional Hardy type inequality for fuzzy integrals

TL;DR

This paper extends two-dimensional Hardy type inequalities to fuzzy integrals using pseudo-analysis, involving set-valued functions and novel pseudo-operations, broadening the scope of integral inequalities in fuzzy and set-valued analysis.

Contribution

It introduces new two-dimensional Hardy inequalities for fuzzy integrals within pseudo-analysis frameworks, utilizing pseudo-addition and pseudo-multiplication based on monotone functions.

Findings

Established a Hardy inequality for pseudo-integrals of set-valued functions.

Derived a Hardy inequality within the semiring $([0, 1], \max, \odot)$ setting.

Extended classical inequalities to fuzzy and set-valued contexts.

Abstract

In this paper, a new two-dimensional Hardy type inequality is given in terms of pseudo-analysis dealing with set-valued functions. The first one is given for a pseudo-integral of set-valued function where pseudo-addition and pseudo-multiplication are constructed by a monotone continuous function $g:[0, \infty ]\to[0, \infty]$. Another is given by the semiring $([0, 1], \max, \odot)$ where pseudo-multiplication is generated by an increasing continuous function.