Abstract–
In this paper we characterize those surjective linear transformations of tropical matrices preserving the set of all weak transitive closures and the set of all strong transitive closures
, respectively. We illustrate that there exist non-surjective linear transformations that preserve
or
. Also, we consider the strongly linear preservers of
and
, respectively.
Acknowledgments
The authors thank Prof. Xianzhong Zhao from Northwest University for his supervision. The authors are grateful to the referee for his/her valuable comments and suggestions.