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From: sthomas@decan.gate.net (S. F. Thomas)
Subject: Re: Fuzzy theory or probability theory? 
Message-ID: <1994Dec7.051926.2915@decan.gate.net>
Organization: Decision Analytics, Inc.
Date: Wed, 7 Dec 1994 05:19:26 GMT
References: <1994Dec3.021337.18334@decan.gate.net> <1994Dec6.143006.18188@newsserver.rrzn.uni-hannover.de>
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mackw@bytex.com wrote:

: In article <1994Dec3.021337.18334@decan.gate.net>, <sthomas@decan.gate.net> 
: writes:
: > I still insist that any utterance "A and not A" has no meaning in 
: > natural language, at least not in the normal sense of the conjunctive
: > "and".  
: > 
: > As a mathematical formalism I have no quarrel
: > with defining the min-max operators the way they have been in the 
: > Zadehian development.  The difficulty I have is when it is asserted that
: > this formalism accurately represents the use of terms in a natural 
: > language.  
: > 
: Good point Mr. Thomas!  You are quite right in asserting fuzzy logic is a 
                                                           ^^^^^^^^^^^^^^^^
: different language than english, and so is boolean logic, arithmetic, etc.
  ^^^^^^^^^^^^^^^^^^
: I think sometimes we get so used to automatically translating that we 
: forget the fuzzy logic rule 

: 	Suspect = Tall AND (NOT)Tall

: is not equivalent to the english description

: 	The suspect is tall and not tall.

: The first is a meaningful (though probably not useful) definition for a 
: general membership function.  The second is a contradictory description for 
: a specific individual.  Using a literal translation from a fuzzy equation 
: to an english statement is as inappropriate as a literal translation from, 
: say, japanese to english.

I would hardly elevate a mathematical formalism to the status of a
language.  The whole fuzzy enterprise is motivated by claims
that it _captures_ a feature of natural language (fuzziness) that is
not captured by bivalent logic.  Fuzzy logic is attempting to _model_
language; it is not a language in its own right.  Any validity to 
which it lays claim must find vindication in how well it does its job
of modelling natural language.  Boolean logic, arithmetic, etc. also
attempt to capture and make precise features of natural language that
are important to all kinds of human endeavors.  Fuzzy logic attempts to 
do the same, and is at least partially successful.  That is laudable, 
and Zadeh deserves our admiration and praise for his master-stroke.
But the min-max calculus brings with it certain paradoxes, among them
the failure of semantic laws -- excluded middle, contradiction, and
self-contradiction -- which should apply regardless of the fuzziness.
Fuzzy theory should give up this idea that the fact of fuzziness in 
natural language is sufficient justification to give up these
basic semantic laws.  Without these laws, axiomatic method goes
completely out the window; no theorem could ever be proved, including
those of fuzzy theory itself.  Surely such disharmony between meta-
language (in the meta-language, fuzzy theory itself proceeds as an 
exercise in bivalent logic) and object-language (which is what is 
populated by fuzzy terms and descriptors) should cause some cognitive 
discomfort.  My claim is that this cognitive discomfort is unnecessary.
Fuzzy theory is salvageable essentially on its own terms, ie. it is
possible to retain the fuzziness in the object language, _and_ to
conform to the semantic laws now flouted by the min-max calculus.

: Wayne Mack
: 	

Cheers!
S.F.Thomas
