Linear preservers of g-row and g-column majorization on $M_{n,m}$

‎Let $A$ and $B$ be $n\times m $ matrices‎. ‎The matrix $B$ is said to be g-row majorized‎ ‎(respectively g-column majorized) by $A$‎, ‎denoted by $B \prec_{g}^{row} A$ (respectively $B \prec_{g}^{column} A$)‎, ‎if every row (respectively column) of $B$‎, ‎is‎ ‎g-majorized by the corresponding row (respectively column) of $A$‎. ‎In this paper all kinds of g-majorization are studied on‎ ‎$\textbf{M}_{n,m}$‎, ‎and the possible structure of their linear‎ ‎preservers will be found‎. ‎Also all linear operators‎ ‎$T:\textbf{M}_{n,m}\rightarrow \textbf{M}_{n,m}$ preserving (or‎ ‎strongly preserving) g-row or g-column majorization will be‎ ‎characterized‎.