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 $g:[0,\mathrm{\infty }]\to [0,\mathrm{\infty }]$ and the second one is given for the semiring $([0,\mathrm{\infty }],sup,\odot )$ 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.