Od: "William Siler" <wsiler@aol.com>
Temat: Re: fuzzy inference
Data: 16 września 2003 13:22

Dmitry A. Kazakov <mailbox@dmitry-kazakov.de> wrote in message news:<sn3ulv89dhf1k9asgmaeorv4o0124vbjgs@4ax.com>...
> 
> There is a large amount of papers devoted to the issue. A decision
> depends on which result of the crisp set theory have to be preserved.
> It is known that the biggest set is preserved by min/max/1-x.
> 
This statement comes from a paper by Bellman and Giertz (1973) in
Information Sciences. However, as is very well known, min/max/1-x do
not obey excluded middle and non-contradiction. The family of fuzzy
logics Jim Buckley and I have published preserves ALL properties of
crisp logic. See

Buckley JJ, W Siler (1998). A new t-norm. Fuzzy Sets and Systems 100:
283-290.

Buckley JJ, W Siler (1999). L-infinity fuzzy logic. Fuzzy Sets and
Systems 107: 309-322.

There was a substantial thread on this topic in comp.ai.fuzzy a few
months ago. Apparently our logic has one fatal flaw;