Re: Adaptative fuzzy systems and classification

david_olmsted@my-dejanews.com
Tue, 22 Sep 1998 01:33:53 +0200 (MET DST)

In article <19980917225131.23681.00000890@ng15.aol.com>,
wsiler@aol.com (WSiler) wrote:
>
> >Using multivalued logic instead of fuzzy logic will solve
> >your problem since multivalued logic has a fundamental
> >level conditional operation where fuzzy logic does not.
>
> I find your comment mistifying. Fuzzy logic is one of a host of multivalued
> logics, ranging from the Zadehan logic (fuzzy logic) at one end of the
spectrum
> to the Lukasiewicz logic at the other. Which multivalued logic are you
> referring to? Or are you referring to a multistate logic, where three or more
> levels are permitted?
>
> And what is a "fundamental level conditioning operation"?
>
> Please enlighten me.
>
> William Siler
>
>

I am referring to the infinitely valued logic which Lukasiewicz developed
which is a superset of the later fuzzy logic. For a history of this
multivalued logic see the page entitled "History of Multivalued Logic" at my
site http://www.neurocomputing.org. Also I assume you mean the fundamental
level CONDITIONAL operation. It is simply the mathematical subtraction
operation which is the negated form of the Lukasiewicz IMPLICATION operation.

The site also shows how multivalued logic operations can be used as the
operations in an adaptive neural network for pattern classification. For this
see the Tectum-Reticular Formation page.

Reference

Philosophical Remarks on Many-Valued Systems of Propositional Logic by Jan
Lukasiewicz in "Polish Logic: 1920-1939", edited by Storrs McCall, Oxford
Clarendon Press (1967)

Sincerely,
David Olmsted

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