For $A,\ B >0$, the chaotic order $A \gg B$ is defined by $\log A \ge \log B$. It is known $A \gg B$ if and only if $A^{-r}\ \sharp_{\frac{r}{p+r}}\ B^p \le I$ for all $r \ge 0$ and $p \ge 0$. We show this by Uchiyama's technique without using Furuta inequality. Furthermore we give an interpretation for the genelarized Furuta inequality, that is, if $A,\ B > 0$ and $A \gg (A^{-\frac{t}{2}}B^pA^{-\frac{t}{2}})^{\frac{1}{p-t}}$ for $p > t \ge 0$, then $$A^{-r+t}\ \sharp_{\frac{\delta+r}{\beta-t+r}}\ (A^t\ \natural_{\frac{\beta-t}{p-t}}\ B^p) \le A^t\ \natural_{\frac{\delta}{p-t}}\ B^p $$ holds for $r \ge 0$ and $0 \le \delta \le \beta-t$. If $t=0$ and $\beta = p$, then this shows the chaotic case of Furuta inequality and the case $t=1$ corresponds to the Ando-Hiai inequality.