Re: Fuzzy Logic - why?

WSiler (wsiler@aol.com)
Wed, 11 Nov 1998 06:26:21 +0100 (MET)

>>"Fuzzy classification evidently violates Aristotle's law of the excluded
>>middle."
>>
>>Yes, this is inherent in any multivalued logical system - in the sense that
>>you can't have it both ways (except in such systems, where of course you
>>can!)
>
>Aristotle's law of the excluded middle should be violated by all means -
>it's quite a bit of nonsence. :)

Sorry, I can't agree that excluded middle is nonsense. I know that al most all
fuzzy people think so, but frankly I think that is mostly sour grapes.
Sometimes (not always) NOT to obey excluded middle and contradiction is quite
counter-intuitive.

An example. I have set up triangular membership functions for Slow, Medium and
Large, all intersecting nicely at the 0.5 point. Intuitively, NOT (Slow OR
Medium) should end up to be Large. But instead, we OR SLow and Medium and get a
curve with a blasted notch in it, and when I NOT that I come up with Large with
an extra half-size triangle stuck off to the side.

Acutally, the problem is not inherent in "any multivalued logic system. The
priciple here is that IF we want to preserve excluded middle and contraction,
and IF we have semantically inconsistent operands, all we have to do is switch
to bounded sum for OR and we are home free. In the example given just above,
using the bounded sum OR makes NOT(Small OR Medium) precisely equal to Large.

William Siler

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