Linear functions preserving row substochastic upper triangular majorization on $R^3$

A real matrix R with nonnegative entries is called row substochastic if each row sum is at most 1. For $x, y\in R^n$, we say that $x$ is row substochastic upper triangular majorized by y (write as $x ≺_sut y$) if there exists a row substochastic upper triangular matrix $R$ such that $x = Ry$. In this paper, the structure of all linear functions $T : R^3\to R^3$, preserving (strongly preserving) $≺_sut$ are characterized