Re: Adaptative fuzzy systems and classification

WSiler (wsiler@aol.com)
Tue, 22 Sep 1998 02:32:39 +0200 (MET DST)

>After checking some publications I am convinced that the multivalued logic
>definitions for AND and INCLUSIVE OR are the same as that for fuzzy logic.
>
I am not sure what you mean by multivalued logic; in my vocabulary, a
multivalued logic is any logic which permits other truth values besides 1 and 0
(true and false). This definition whould include an infinite variety of logics.

Certainly Lukasiewicz was a major pioneer in such logics. His ideas changed
somewhat as the theory developed, which can certainly lead to confusion. He did
indeed use max-min among others, but did not develop it as Zadeh did, and
failed to make the connection to set-theoretic operations which Zadeh developed
so effectively. George Klir says "The insufficiency of any single
infinite-valued logic, and therefore the desirability of a varety of these
logics, is connected with the notion of a complete set of logic primitives."

I can't agree that Zadehan fuzzy logic lacks the implication operator. Klir and
Yuan list a whole slew of possible implication operators which can be used in
fuzzy logic, including three variations on the Lukasiewicz implication.
Personally, I avoid the implication operator like the plague, and use direct
assignment in the consequents of rules, as does Sugeno.

I think it unfortunate that Lukasiewicz developed his ideas using negation and
implication as primitives.

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