I have a possible explanation but I am not sure. Since the operation
x+y-xy is a PROBABILISTIC OR, the membership values for all variables
are based on their probability of occurance.. eg.
SET Slow_speed { speed,membership} can be
{(0,1.0), (40,.75), (50,.5), (100,1.0)}
These values could be based on their probability.. ie how many people
consider a particular speed to be slow etc.
Therefore when we do a X or X = X+X- X.X this is greater than X.
Interpretation could be,
if more and more people start giving inputs on a particular speed to
be slow, gradually the probability of it being considered slow will
increase. when the number of ors on a variable extends to infinity,
the membership tends to 1.0 . I think this is a valid explanation.
I do not have any source for this interpretation but this is just
my understanding.
Do let me know if I am correct or not...
cheers,
Kamal
>
> 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
>
> From: bryce@albatross.co.nz
> >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"
> >
> >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
> http://www.mar.dfo-mpo.gc.ca/science/mesd/he/staff/silvert/silvert.html
>
>
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