On Else Clauses and Rule-Chaining

Bob Dalton (red@swl.msd.ray.com)
Mon, 17 Nov 1997 02:29:02 +0100 (MET)

I agree that, given membership functions for "old" and "young" as
premises, it is wasteful to use "not old" as a premise. I think
using "not old" is the same as using an else clause.

For chaining in rulebases, I use a generalized modus ponens measure

max (0, min (v(a)) + v(a => b) - 1),

where v(a) is the fuzzy measure of the premise, (usually = min {v (ai) },
when there are more than one premise), and v(a => b) is a fuzzy measure
of the relevance of the implication itself.

Note that using this measure, the final relevance factor in a chain can
never be larger than the initial relevance factor for any hypothesis
established in the course of reaching that final state. That is, the
measure is strictly decreasing along the chain, except in crisp cases.

This makes the measure very useful in cutting off candidate chains
via thresholds.

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Robert E. Dalton, Ph. D. email: red@swl.msd.ray.com

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