# Linear operators that strongly preserve regularity of fuzzy matrices

Mathematical Communications, Vol.15 No.1 June 2010. -

An $n\times n$ fuzzy matrix $A$ is called {regular} if there

is an $n\times n$ fuzzy matrix $G$ such that $AGA=A$. We study the

problem of characterizing those linear operators $T$ on the fuzzy

matrices such that $TX$ 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 $TX=PXQ$ or $TX=PX^tQ$ for

all fuzzy matrices $X$.

generalized inverse of a matrix; fuzzy regular matrix; linear operator

Author: Kyung-Tae Kang - ; Department of Mathematics, Jeju National University, Jeju, Korea Seok Zun Song - ; Department of Mathematics,

Source: http://hrcak.srce.hr/