Re: Std.1788-Inner operations and RDM

[Walter Mascarenhas <walter.mascarenhas@xxxxxxxxx>]

Dear Mehran,

   The problems caused by dependency are well known,

and I believe you should pay more attention to what

George, John, Ned, Vladik and Vincent are saying.

   As George also said, improvements in this area would

certainly be welcome, and I support your attempts to

deal with this problem. However, I also believe that you
could elaborate your thoughts a bit more and write them

more clearly. For instance, it is hard to understand
your diagrams. A discussion in a mailing list like

this one is certainly not the best way to promote

your ideas. 

   I also believe that it would be important to turn

your ideas into real software, so that we could

verify their effectiveness in practice. Once you

have your idea encoded in a software library

we would be able to learn more from them.

  We already have implementations of the

standard by Oliver Heimlich and Marco Nehmeier,

and whenever I find the time I will also present

one implementation. It would be nice to compare

your implementation with them. It would be

great if we could incorporate your ideas into them.

  There are many issues involved in the practical
implementation of interval arithmetic, and in the
elaboration of an standard, that you may be overlooking.
By working on the practical implementation of your

ideas, and trying to convince people to use your
software,  I believe that you will have a better

perspective of the tradeoffs involved.

               walter.

On Wed, Sep 30, 2015 at 3:25 AM, Mehran Mazandarani <me.mazandarani@xxxxxxxxx> wrote:

Dear Vladik, George, John,Svetoslav,Evgenija,Vincent, and other members

First of all, thank you for your very kind attention and valuable comments.

George wrote that "To exploit context knowledge of the _expression_ in which “-“ appears requires MUCH more sophisticated machinery,..." and " The subtraction operator sees SUBTRACT(X, Y)"

Let me don't agree with you, because the subtraction operator can also see SUBTRACT (X,Y,K), K=0,1. K=0 means X and Y are of the same source, otherwise they are of the different source.

About the inner operations and using them, I would like to bring to your attention some issues. Although the inner subtraction and addition operations possess some advantages, they have themselves a few shortcomings. The shortcomings can be termed as Restoration issue and Self-Reduction issue. Please see the attachment. As you can see, the Self-Reduction is a major issue of inner addition. Consider the interval [1 4] and try to add it to itself using inner addition, what do you see?
You see the result as [1 4] {+} [1 4]=5, where {+} - assume - means inner addition.
What the result means is that the uncertainty vanishes. That is actually odd!!. For more clarification see the example of a Box and forces in the attachment.
Additionally, Indeed, I subscribe to Vincent's view.

I appreciate your kind attention and consideration.

Warmest regards,

Mehran Mazandarani
Department of Electrical Engineering
Ferdowsi University of Mashhad, Mashhad, Iran.
homepage:http://mehran.mazandarani.fumblog.um.ac.ir/
http://works.bepress.com/mehran_mazandarani
IEEE Member, me.mazandarani@xxxxxxxx