# Re: Ways to evaluate fuzzy predicates

WSiler (wsiler@aol.com)
Sun, 15 Nov 1998 22:41:13 +0100 (MET)

>I was wondering what systems people use to evaluate fuzzy predicates. I
>have seen definitions such as:
>
> A AND B=min(A,B)
> A OR B=max(A,B)
>
>and am wondering what alternative definitions exist. Are there any means
>of assigning different weights to A and B, for example? Can fuzzy
>implication be dealt with in analogous terms to normal Boolean
>implication? i.e. does this hold:
>
> A->B == NOT(A) OR B == max(1-A,B)
>
>

>I was wondering what systems people use to evaluate fuzzy predicates. I
>have seen definitions such as:
>
> A AND B=min(A,B)
> A OR B=max(A,B)
>
>and am wondering what alternative definitions exist.

There is a whole family of alternatives, but max-min dominates; with anty other
AND/OR definitions, the AND of several clauses in a rule with a complex
antecedent drizzles down to zero, and the OR of several clauses drizzles up to
one. One alternative is the "probabilistic" a AND b = a*b, a OR b = a+b -
a*b.

> Are there any means of assigning different weights to A and B, for example?

Not that I know of.

>Can fuzzy implication be dealt with in analogous terms to normal Boolean
>implication? i.e. does this hold: A->B == NOT(A) OR B == max(1-A,B)

There is a whole slew of fuzzy implications, of which you list one; Klir and
Yuan list over a dozen. However, their utility in practice is up for grabs.
This is to complicated to address here - I've got to walk my dogs!

William Siler

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