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From: sthomas@decan.com (S. F. Thomas)
Subject: Re: Q: Implementing Fuzzy OR
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Date: Sat, 12 Apr 1997 11:12:49 GMT
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WSiler (wsiler@aol.com) wrote:

: There is an infinite number of different ways of ORing fuzzy logical
: expressions, which return quantities between zero and one. With a few
: exceptions, the values returned are bracketed by the Zadeh operator [A OR
  ^^^^^^^^^^
<snip>
I wasn't aware of any.  What are they, and how are they justified?

(( cuts ))

: In other words, if you have two rules with the same consequent, and the
: tendency is for both rules to fire or neither rule to fire, the Zadeh OR
: is fine. 
: If one or the other rule tends to fire, but not both rules at
: once amd not for neither rule to fire, the Lukasiewicz OR is good. If the
: rules tend to have a random firing pattern with relation to each other,
: the probabilistic OR is probably your best bet.

: In our experience, the tendency is for both rules to fire or neither rule
: to fire, so we use the Zadeh OR by default. However, there is provision
: for other ORs as well to be used when they are needed.

: Hope that helps. I may get an argument from Maurice Clerc or SF Thomas,
: though. I'd be glad to hear the thoughts of others on this matter.

<chuckle> Sounds like you are begging for it...

But seriously, I pretty much agree with what you say, although I like
my terminology better, namely the notions of _semantic_ consistency
(positive and negative), and _semantic_ independence.  One can have
statistical correlation (positive or negative) in the presence of 
semantic independence.  For example, consider an application
where there are two rules, one based on the volume (cubic dimension)
of a piece of cargo, the other based on the weight of the piece. I
would expect the firing of the two rules to be correlated because
of the statistical correlation between volume and weight over disparate
types of cargo.  At the same time, the two rules are _semantically_ 
independent, hence if they have the same consequent, one wishes to 
evaluate the consequent not based merely on the stronger of the 
two antecedents (max rule) but based on a combination of the two 
(product-sum rule).  Therefore, whether or not there is statistical 
correlation in the firing of the two rules, they should be treated 
as being _semantically_ independent.

I can also think of situations where there is statistical _in_dependence
in the presence of semantic _de_pendence, further emphasizing the
point that the choice of rule for the OR operator must be based on
semantic considerations rather than on real-world statistical
contingency relations.  

Having said that, I hasten to add that semantic consistency/independence 
itself stems from a notion of statistical correlation, but having to do 
with the language-use phenomenon, as distinct from the real-world 
phenomenon which is being described/controlled.

These are of course fine distinctions, but it is hard to avoid
them when foundational issues are being addressed.  They may even
impinge on the engineering common-sense which must be deployed
in real-world applications.

: Bill Siler

Regards,
S. F. Thomas


