2011/8/4 Lee Winter
<lee.j.i.winter@xxxxxxxxx>
On Wed, Aug 3, 2011 at 2:56 PM, Michel Hack <
hack@xxxxxxxxxxxxxx> wrote:
> (1) Intervals as imprecise single values.
>
> (2) Intervals as bounded (or semibounded) ranges of separate values.
"separate values"?
I do not have an exact definition of "separate values" nor of the second type mentioned by Michel, but I have a simple example to present where both types may be used:
The potential start and end times of tasks in a project management program or a real time embedded system might be represented as intervals. For example a task may be started any time within [t1, t2] or start any time after t1 which is represented as [t1, infinity]. These intervals belong to the second type described by Michel which are ranges, possibly very wide ranges, and not an imprecise value. A task with duration d that must start within [t1,t2] and end within [t3,t4] will require us to solve
[t1+d,t2+d] intersect [t3, t4]
to find the possible starting and ending dates for this specific task.
Now if the duration of the task is not precisely known (first type described by Michel) but is given as [d-delta, d+delta] then we have the two types mixed together in one application.
Michel has made this point several times and I agree with him that the two types are different and may require us to think differently. They may be used together as in the example above or separately.
--
Hossam A. H. Fahmy
Associate Professor
Electronics and Communications Engineering Department
Cairo University
Egypt