# Re: Algorithm for fuzzy "OR" calculations?

David Kastrup (dak@fsnif.neuroinformatik.ruhr-uni-bochum.de)
Mon, 2 Mar 1998 18:43:08 +0100 (MET)

"Alfred Kellner" <alfkellner@magnet.at> writes:

@> bryce@albatross.co.nz wrote in <6cqulc\$hc0\$1@nnrp2.dejanews.com>...
@> > Does anyone have an algorithm for calculating a fuzzy 'OR' on x number of
@> > values, given the formula X OR Y = x+y-xy (as opposed to the more standard
@> > fuzzy definition of X OR Y = max(x,y).
@> >
@> > As an example, a OR b OR c can be calculated given the idea that <a OR b OR
@> > c> is like <<a OR b> OR c>, ie:
@> >
@> > "(a + b -ab) + c -(a + b -ab)c"
@> > or
@> > "a + b + c -ab -bc -ac +abc"
@> >
@>
@> I doubt the Algorithm X OR Y = x+y-xy
@> since
@> X OR Y <= X
@> and X OR Y <= Y
@> must hold true.
@> When i.e. Y=X=0.7 then x+y-xy == 0.7+0.7-0.7*0.7 == 0.91
@> So ( 0.91 <= 0.7 ) == false !!
@>
@> Am I fuzzy missing something ?

Yes. At the very least, you are confusing AND and OR. X OR Y is *at
least* as true as either X or Y are, so its truth value is expected to
be at least that of X and Y, not at most.

As to the original question: I think that just using associativity
and pairing the truth values successively will usually turn out easier
and requiring less operations than fighting for the general formula
for n variables.

```--
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut für Neuroinformatik, Universitätsstr. 150, 44780 Bochum, Germany
```