Regarding Equitable Colorability Defect of Hypergraphs

\noindent Azarpendar and Jafari in 2020 proved the following inequality $$\chi ({\mathrm{K}\mathrm{G}}^r(\mathcal{F},s))\ge \lceil \frac{{\mathrm{e}\mathrm{c}\mathrm{d}}^r(\mathcal{F},\lfloor \frac{s}{2}\rfloor )}{r-1}\rceil ,$$ and noted that it is plausible that the above inequality remains true if one replaces $\lfloor \frac{s}{2}\rfloor$ with $s$. \noindent In this paper, considering the relation ${\mathrm{e}\mathrm{c}\mathrm{d}}^r(\mathcal{F},x)\ge {\mathrm{c}\mathrm{d}}^r(\mathcal{F},x)$ which always holds, we show that even in the weaker inequality $$\chi ({\mathrm{K}\mathrm{G}}^r(\mathcal{F},s))\ge \lceil \frac{{\mathrm{c}\mathrm{d}}^r(\mathcal{F},\lfloor \frac{s}{2}\rfloor )}{r-1}\rceil ,$$ no number $x$ greater than $\lfloor \frac{s}{2}\rfloor$ could be replaced by $\lfloor \frac{s}{2}\rfloor$.