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Re: P1788.1/M001.01



Dear Vladik and members
Thank you for your reply to my questions. But let me don't agree with your calculations. Because you told "... we get exactly the results of interval arithmetic -- and exactly what we want when we are estimating the range of the possible values."
First of all, it seems that the calculation is based on Moor's approach which leads to misleading us in some cases. Let me explain it based on the first case of subtraction [1,3]-[1,3]. For calculating this case you obtained the result [-2,2] as the exact result and possible range this result can be correct if the values correspond to different sources. However, the result does not show the possible values if they correspond to a same source. We are misled if the approach take us to a space in which the values are (actually) impossible. In the mentioned case if we deal with a same source all values [-2,2] except of zero are impossible. See the attachment please.
That's why the Moor's approach is not a reliable approach. Using that approach leads to high cost for implementing everything and too much conservatism. This is true about other operations and cases.
One may be wondering then what should be considered for using as an alternative/reliable approach?
My answer is what was proposed by Prof. Andrzej Piegat, that is called Relative-Distance-Measure variables to get the result granule and in fact exact solutions.
It would be explained in next post.
Any way, I think such calculation, [1,3]-[1,3]=[-2,2], or [-1,1]*[-1,1]=[-1,1], neither give us the exact results nor real possible solutions.


I appreciate your kind opinion about the matter.
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











On Fri, Sep 25, 2015 at 12:23 AM, Kreinovich, Vladik <vladik@xxxxxxxx> wrote:
This is just a simplified version of the general interval standard, so the answers should be exactly the ranges of the corresponding functions, in the first case, the range of f(x1,x2) = x1 - x2 when x1 is in [1,3] and x2 is in [1,3]. Due to monotonicity, we have the range [1-3,3-1] = [-2, 2].

In the second cases, similarly, we have the range of the function f(x1, x2) = x1 * x2 when x1 is in [-1, 1] and x2 is in [-1,1], the range is [-1, 1].

In both cases, there is no need for rounding, so we get exactly the results of interval arithmetic -- and exactly what we want when we are estimating the range of the possible values.

-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Mehran Mazandarani
Sent: Thursday, September 24, 2015 2:37 PM
To: John Pryce <j.d.pryce@xxxxxxxxxx>
Cc: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Re: P1788.1/M001.01

Dear John
Thank you for your advice. But I just have the simplified standard document (Clause 4.pdf) which ends by the page 6.
Could somebody answer the two questions concretely.

Cordial regards,


On 9/24/15, John Pryce <j.d.pryce@xxxxxxxxxx> wrote:
> Dear Mehran
>
> On 24 Sep 2015, at 15:14, Mehran Mazandarani
> <me.mazandarani@xxxxxxxxx>
> wrote:
>> I have some simple questions about the simplified standard
>> P1788.1/M001.01.
>> Based on the standard P1788.1/M001.01, 1. What is the output of
>> [1,3]-[1,3]=?
>> 2. What is the output of [-1,1] multiply by [-1,1]?
>
> I think these are answered by page 9 lines 10-13, in §4.4.4, of the
> circulated Clause 4.
>
> Regards
>
> John Pryce


--
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

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