
Section 4.6 Interval matrices and interval vectors on a screen 123
Theorem 4.25. Let fV , R, g be a completely and weakly ordered vectoid with the
neutral elements o and e if a multiplication exists, and let fS, g be a symmetric
screen of fV , R, g. Further, let fIT, }
C
, }
g be a monotone upper screen ringoid
of fIR,
+
,
g with respect to . Consider the two semimorphisms : PV ! IV
and } :
IV ! I S .ThenfIS, IT, , g is a weakly ordered vectoid with respect to
. It is multiplicative if fV , R, g is. The neutral elements are Œo, o and Œe, e. With re-
spect to , fIS, IT, , g is an inclusion-isotonally ordered monotone upper screen
vectoid of