Re: What is the intuitive meaning of the strict norm and co-norm

Thomas Whalen (dscthw@panther.gsu.edu)
Mon, 11 Jan 1999 13:55:10 +0100 (MET)

How far beyond the opposite side of a one-meter gap can you reach with two
planks with lengths x and y?
Answer: WEAK(x,y)

If you have two planks each of 1 meter length, ant I take away a piece of length
x from one plank and a piece of length y from the other, and you try to use
what's left to bridge the one-meter gap and cover as much as possible of the
opposite side, how much of the first meter of the opposite side will remain
uncovered?
Answer: STRONG(x,y)
(If min(x,y)>0 you can't bridge the gap and the whole meter is uncovered;
if min(x,y)=0 then you can cover min(1-x,1-y) of the opposite side,
leaving max(x,y) uncovered.)

Andrei Heilper wrote:
>
> The characterization of t-norm is that
> WEAK(x,y) <= T(x,y) <= min{x,y} where WEAK(x,y) = min{x,y} if max{x,y}
> =1 and 0 otherwise
> Similarly a t-conorm satisfies
> max{x,y} <= S(x,y) <= STRONG{x,y} where STRONG(x,y) = max{x,y} if
> min{x,y} =0 and 1 otherwise
> Are there any significant examples where we can attach a meaningful role
> for WEAK and/or STRONG?
>
> Andrei Heilper
>
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-- 
Tom Whalen     whalen@gsu.edu  http://www.gsu.edu/~dscthw
Professor of Decision Science 
The Georgia State University         "First things first, but not 
Atlanta, GA 30303-3083 USA         necessarily in that order"  - Dr. Who

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