RE: Undefined behaviour (Was: Definition of intervals as subsets...)

["Kreinovich, Vladik" <vladik@xxxxxxxx>]

The explanation is simple: in Kaucher arithmetic, the interval [5,2]
DOES NOT mean {x: 5<= x <=2}, this interpretation would lead to an empty
set. 

You want to look for pages on modal intervals. Just FYI, I placed my
unpublished report on modal intervals (with explanations aimed at
engineers) on my webpage, as http://www.cs.utep.edu/vladik/modal.pdf
(just read Part I, Part ii is re how to incorporate probabilities). 

-----Original Message-----
From: Dan Zuras Intervals
 
> For example, the Kaucher interval addition
> 
>     [a,b]+[c,d]=[a+c,b+d]
> 
> is the same as the classical formula except it
> relaxes the constraint a <= b and c <=d, i.e.,
> 
>     [5,2]+[3,9]=[8,11]
> 
> is the correct modal result.
> 
> . . .
> 
> Sincerley,
> 
> Nate Hayes
> Sunfish Studio, LLC

	Nate,

	Am I missing something here?

			[5,2]+[3,9]=[8,11]

	Can it really be that the sum of {x | 5 <= x or x <= 2}
	and {y | 3 <= y <= 9} is {x+y | 8 <= x+y <= 11}?

	Stated another way, can it really be that the sum of a
	bifurcated interval of infinite width & an ordinary
	interval of width 6 is an ordinary interval of width 3?

	This appears non-intuitive at best or wrong at worst.

	Can you explain this result?

	Thanks,

				Dan