2009/9/21 Vincent Lefevre
<vincent@xxxxxxxxxx>
> Standardising midrad has difficulties not present with infsup (non-
> uniqueness of finite precision interval hull,
That's why it may be interesting to have it standardized, so that
different midrad implementations do not behave too differently.
I agree with Vincent. We should study MidRad more before making any quick assumptions on whether it should be included or not. If it becomes clear that its exclusion may lead to some future chaos then we should rise up to the challenge and do the extra work needed to get a comprehensive standard.
> lack of representation for semi-infinite intervals);
This one is not a difficulty. On the contrary, it is simpler: as
soon as the error bound becomes infinite, return R.
On this, however, I disagree with Vincent. What you say is correct for the first domain described by Michel at the start of this thread
"One domain of application is operating with uncertain numbers, where an
interval represents a single numeric value with bounded uncertainty.
In this domain MidRad and InfSup are logically interchangeable"
but not for the second domain
"A totally different domain is that of intervals representing ranges of
different, individually-precise, numeric values, where that range may
be unbounded on one or both sides. InfSup is the only flavour that
can handle this domain, and semibounded intervals can only be converted
to totally-unbounded MidRad from, i.e. Entire."
Michel made a very important observation by separating those two domains.
Regards,
--
Hossam A. H. Fahmy
Assistant Professor
Electronics and Communications Department
Cairo University
Egypt