Re: Problem with fuzzy rule implication

WSiler (
Sun, 9 Nov 1997 02:34:42 +0100 (MET)

>> I am currently working on a fuzzy rule engine in Java. One of the
>> problems I am having is deciding when the alternate clause of a
>> consequent should be invoked.

I'm afraid that Chris has not addressed the original problem.

Our system does not provide for the if ... then ... else ... construct, partly
because we do not have a good solid answer to the problem Michael poses for
fuzzy rules. I understand that Earl Cox's system does permit the if ... then
... else ... construct. Earl, how about addressing this problem?

The problem is further complicated by the use of rule-firing thresholds,
sometimes used to avoid exploring paths of low confidence in which we are
uninterested. It is still further complicated by the use of rule confidences,
something we often use either because we are really not sure the rule is
valid, or as a device for guiding a search.

Since I don't have experience with if-then-else rules, the following is very
tentatively offered.

Suppose that the confidence that the antecedent is true is alpha, and that the
rule confidence is beta. If neitheralpha AND beta nor (1 - alpha) AND beta is
greater than the rule firing threshold, the rule is not fired at all. If alpha
AND beta exceeds the threshold, fire the first consequent with confidence
alpha AND beta; if (1 - alpha) AND beta exceeds the threshold, fire the second
consequent with confidence (1 - alpha) AND beta.

Note that it is quite possible that both alpha AND beta and (1 - alpha) AND
beta will exceed the threshold. I suppose that in this case one would fire
both consequents with their respective confidences.

All this makes me happy that we only use if-then rules!

Bill Siler