Algorithm for fuzzy "OR" calculations?

Bill Silvert (
Fri, 6 Mar 1998 16:26:18 +0100 (MET)

I'm interested in the series of postings in reply to this question, none
of which has touched on the matter of greatest interest to me, namely
what does this OR operator signify? It has the proporty that as the
number of values being OR'ed increases, the OR approaches 1. For
example, 0.5 OR 0.5 = 0.75, 0.5 OR 0.5 OR 0.5 = 0.875, etc.

One can of course define any operators one wants, but an OR operator
such that x OR x > x seems quite peculiar, and I am wondering what this
one really represents.

Bill Silvert

>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"
> "a + b + c -ab -bc -ac +abc"
>The tricky part is that I need this to work for any number of values, not
>just two or three. I am actually planning to use this in a Delphi
>application, but examples in C would be fine.

Bill Silvert, Habitat Ecology Section, Bedford Institute of Oceanography,
P. O. Box 1006, Dartmouth, Nova Scotia, CANADA B2Y 4A2, Tel. (902)426-1577