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About Sun's f95 with Interval Support
# Interval FAQ

Dominique Faudot -- Interval arithmetic of functions?

From Dominique Faudot
(faudot@u-bourgogne.fr):
## What do X < Y and X > Y mean?

I have 2 intervals X = [a, b], and Y = [c, d].
What do X < Y and X > Y mean?
I am thinking specially when Y is a degenerate interval with c = d.
Dominique Faudot

(zkulpa@zmit1.ippt.gov.pl):
Standard definition (where X = [a, b] and Y = [c, d]):

X < Y <=> b < c
X > Y <=> a > d

Zenon Kulpa

(aha2@eecs.Lehigh.edu),
Lehigh University:
There are two possible comparisons for intervals. These are
*certainly* and *possibly* relations. If you want to
make sure that X > Y then you should use the *certainly*
relation, which means that a > d.

If you want you can use *possibly* greater than comparison
by checking b > c.

Less than relations are similar to greater than. I hope this helps you.

Ahmet Akkas

(vellino@nortelnetworks.com):
Another way of saying this might be: it depends on whether you
interpret an interval to mean "there is a point that lies between
the bounds" and the relation between two intervals to be a relation
between the two points ("possibly" relations) or whether you mean
by an interval "the set of all points between the bounds" and the
relation between two intervals to be a relation between two sets
("certainly" relations).

Cheers - André Vellino

(bill.walster@eng.sun.com),
Sun Microsystems:
The definition of an interval must be invariant.

Formal definitions for all certainly, possibly, *and* set relations are
contained in a specification for support of intervals in Fortran.
Earlier drafts of this specification have been posted to
www.mscs.mu.edu/~globsol/walster-papers.html

A few implementation issues are in the process of being clarified in the
final draft, which will also be posted to the above URL. With respect to
the current question about the interpretation of ordering relations
between intervals, the draft posted above will suffice.

Regards to all,

Bill Walster

(yakovlev@globlab.msk.su):
All cases of two intervals comparing were investigated in my paper:
Alexander G. Yakovlev,
*Classification approach to programming of localizational (interval)
computations*, Interval Computations, 1(3), 1992, pp. 61-84.
If don't have this issue, I can send you its TeX version.

Best wishes,

Alexander Yakovlev

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About Sun's f95 with Interval Support
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