
Section 4.4 Interval vectors 107
4.4 Interval vectors
Similar to Section 4.3, we are now going to derive easily implementable formulas for
the interval operations occurring in vectoids.
Again let fR, C, , g be a completely ordered or weakly ordered ringoid. Then
fV
n
R, R, g, fM
n
R, R, g,andfV
n
R, M
n
R, g, where the operations and the order
relation are defined by the usual formulas, are completely ordered (resp. weakly or-
dered) vectoids. In particular, fM
n
R, R, g is multiplicative.
Moreover, by Theorem 2.11 the three power sets fPV
n
R, PR, g, fPM
n
R, PR, g,
and fPV
n
R, PM
n
R, g are inclusion-isotonally ordered vectoids (with the empty set
excluded