For Motions 39,40,41: current text of clauses 1 and 2

[John Pryce <j.d.pryce@xxxxxxxxxx>]

P1788

To aid the vote on motion 39 (subclauses 1.1 to 1.6) and the ongoing discussion on motions 40, 41, here is the current text of clauses 1 and 2, with changes resulting from comments and discussion since the motions were submitted. A couple of points:

(1, trivial)
It was suggested there should be a section on Normative References near the beginning, so I put a stub for it in clause 1 just after 1.1 "Scope". It is not numbered yet so as not to upset the existing numbering during the vote. We shall need to vote on it later.

(2, major)
In 1.7-1.8 which are the subject of motion 40, I have reservations about the paragraph
> Specifically, if the data before and after the unit of transformation are regarded as sets of mathematical intervals, the transformed form of all combinations of the elements (the real values) represented by the prior set shall be a member of the posterior set.

because 
(a) It is a description of how operations in the set-based flavor work, and even there only applies to arithmetic operations. Arithmetic operations in the Kaucher flavor behave like that on proper intervals, but not on improper ones.
(b) The same thing is said in math symbols in the set-based Level 1 text, specifically 8.4.3 "Interval-valued functions", and I think it is wise to avoid duplication if possible.

Nick Maclaren, author of 1.7-1.8, suggested revised wording on 9th Dec (off-line discussion), but it still was set-based -- I think it would be hard to interpret it for Kaucher improper intervals.

I suggested to Nick: why not shorten this, just saying that the way a "unit of transformation" works depends on the kind of transformation ("convexHull" behaves differently from "+") as well as the flavor, and is specified precisely in each flavor's part of the standard. 

I think that solves problems (a) and (b). But I don't seem to have had his response yet.

Looking at clauses 1 and 2 together, I wonder if Nick would find it easier to re-draft, if the current 1.7 and 1.8 came after 2.4 "Operations", at which point one can if wished mention the FTIA, as well as flavors. But maybe that would mix up too many ideas. Comments welcome.

John Pryce

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