A matrix $A$ is said to have $𝐗$-simple image eigenspace if any eigenvector $x$ belonging to the interval $𝐗=\{x:\underline{x}\le x\le \overline{x}\}$ containing a constant vector is the unique solution of the system $A\otimes y=x$ in $𝐗$. The main result of this paper is an extension of $𝐗$-simplicity to interval max-min matrix $𝐀=\{A:\underline{A}\le A\le \overline{A}\}$ distinguishing two possibilities, that at least one matrix or all matrices from a given interval have $𝐗$-simple image eigenspace. $𝐗$-simplicity of interval matrices in max-min algebra are studied and equivalent conditions for interval...