# Re:Fuzzy logic operator evaluation.

From: Walter Banks (walter@bytecraft.com)
Date: Tue Aug 21 2001 - 06:36:34 MET DST

• Next message: Stephan Lehmke: "Re: Thomas' Fuzziness and Probability"

WSiler@aol.com wrote:

> I<< > In article , Robert Dodier writes:
> > >
> >> Any such definition must ignore the relation between elements in a
> compound: if truth(B')=truth(B), then in any proposition containing A and B,
> I can swap in B' in place of B, and get exactly the same truth value for the
> compound; whether the elements are redundant, contradictory, or completely
> unrelated doesn't enter the calculation.
> >>
>
> This is easily achieved if we see that Short, Medium and Tall are all
> negatively associated. In my system, if A and B are not semantically
> inconsistent, we can use any multivalued logic we please including Zadeh's;
> but if A and B are semantically inconsistent, we MUST use A OR B = min(1, a +
> b), and A AND B = max(0, (a + b) - 1). Applying this to Earl's example, Short
> OR Medium OR Tall = 1, and Short AND Medium AND Tall = 0.
>
> This logic is not truth functional; we have to parse the (complex)
> proposition to see what logic we should use. But the results give us a
> multivalued logic which makes sense both mathematically and to the layman.

Most of us have at one time or another been shocked it the simplistic
nature of min and max to evaluate fuzzy 'AND and 'OR. We have been
equally surprised at the effectiveness of this method of combining
lingustic variables in practical applications.

The following table compares the results of the proposed operators
with the common min max inplimations. (The table was created with
an EXCEL spreadsheet I would be happy to email to anyone who
wishes to play with other ideas)

Fuzzy logic operator test

a b min(a,b) max(a,b) max(0,(a+b)-1) min(1,(a+b))

0 0 0 0 0 0
0 0.25 0 0.25 0 0.25
0 0.5 0 0.5 0 0.5
0 0.65 0 0.65 0 0.65
0 1 0 1 0 1
0.25 0.25 0.25 0.25 0 0.5
0.25 0.5 0.25 0.5 0 0.75
0.25 0.65 0.25 0.65 0 0.9
0.25 1 0.25 1 0.25 1
0.5 0.5 0.5 0.5 0 1
0.5 0.65 0.5 0.65 0.15 1
0.5 1 0.5 1 0.5 1
0.65 0.65 0.65 0.65 0.3 1
0.65 1 0.65 1 0 0.65 1
1 1 1 1 1 1

Walter Banks

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