Original scientific paper

Linear operators that strongly preserve regularity of fuzzy matrices

Kyung-Tae Kang ; Department of Mathematics, Jeju National University, Jeju, Korea
Seok Zun Song ; Department of Mathematics, Jeju National University, Jeju, Korea
Young Bae Jun ; Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju, Korea

Abstract

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 $T(X)$ 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 $X$.

Keywords

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

Hrčak ID:

53233

URI

https://hrcak.srce.hr/53233

Publication date:

10.6.2010.

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