Re: Usage of triangular norms

Vladik Kreinovich (vladik@cs.utep.edu)
Sun, 1 Nov 1998 21:37:10 +0100 (MET)

The explanation is very simple: if you start with an s-norm max, you
will get sup, but if you start with any other s-norm, e.g., with a+b-a*b,
and you apply it infinitely many times, you get identically 1.

Example: if you have an infinite number of values all equal to 0.5,
then max(0.5,0.5,...)=0.5, while if you use a+b-a*b, you get 0.5 o
0.5=0.75; ythen 0.75 o 0.5=0.875, etc., and in the limit of infinitely
many elements, you get 1.

> The AND/OR operations are represented using t-norms and s-norms which
> replace and generalize the min/max operations.
>
> Nevertheless, when defining the composition of relations (and all the
> operations derived from it, including the extension principle) the
> definitions still preserve the sup operations, so we have something
> like,
>
> (R1 o R2) (x,z) = sup_y t(R1(x,y), R2(y,z))
>
> while I would expect that the "sup" operation would be replaced by some
> infinite extension of an s-norm.
>
>
> Andrei Heilper

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