
118 Chapter 4 Interval arithmetic
4.6 Interval matrices and interval vectors on a screen
We begin with the following characterization of IM
n
S.
Theorem 4.23. Let fR, C, , gbe the completely and linearly ordered ringoid of real
numbers and fS, ga symmetric screen of R. Consider the completely ordered ringoid
of matrices fM
n
R, C, , gwith the neutral elements O and E and the semimorphisms
: PM
n
R ! IM
n
R and } : IM
n
R ! IM
n
S.ThenfIM
n
S, }
C
, }
, , g is a
completely ordered ringoid with respect to . The neutral elements are ŒO, O and
ŒE, E. With respect to , IM
n
S is an inclusion-isotonally ordered monotone upper
screen ringoid of IM
n
R.
Proof. Theorem ...