Liapounoff type inequality for pseudo-integral of interval-valued function

Abstract

In this paper, two new Liapounoff type inequalities in terms of pseudo-analysis dealing with set-valued functions are given. The first one is given for a pseudo-integral of set-valued function where pseudo-operations are given by a generator g:[0,∞]→[0,∞] and the second one is given for the semiring ([0,∞],sup,⊙) with generated pseudo-multiplication. The interval Liapounoff inequality is applied for estimation of interval-valued central g-moment of order n for interval-valued functions in a g-semiring.

Keywords

• semiring
• interval-valued function
• pseudo-integral of an interval-valued function
• liapounoff type inequality
• interval-valued central g-moment of order n