Linear operators that strongly preserve regularity of fuzzy matrices

Abstract

An $ntimes n$ fuzzy matrix $A$ is called {regular} if there is an $ntimes n$ fuzzy matrix $G$ such that $AGA=A$. We study the problem of characterizing those linear operators $T$ on the fuzzy matrices such that $T(X)$ is regular if and only if $X$ is. Consequently, we obtain that $T$ strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices $P$ and $Q$ such that it has the form $T(X)=PXQ$ or $T(X)=PX^tQ$ for all fuzzy matrices $X$