Re: Consistency of fuzzy rules

From: Yaochu Jin (ftrjin@mail.ipm.net)
Date: Wed Oct 17 2001 - 09:31:22 MET DST

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    >
    >WSiler@aol.com wrote:
    >
    >> I see no reason why different consequents mean necessarily that the
    >> rules are inconsistent.
    >
    >I agree.
    >I even would go one step further: rules are never inconsistent.
    >Inconsistency only arises when rules contradict domain knowledge.
    >This is irrespective of whether the rules are interpreted as
    >Mamdani-like rules or as implications.

    This argument itself is inconsistent. Remind that fuzzy rules are believed to be
    able to extract knowledge from data. If rules are never inconsistent, how can
    rules be inconsistent with domain knowledge, which can usually be represented by
    fuzzy rules? Just an example. From data, you get two rules:

    R1: If speed is high and distance is short, brake sharply (to stop)
    R2: If speed is high and distance is short, brake slightly (to stop)

    These two rules, in my view are inconsistent. (How inconsistent they are depends
    on the definition of the membership functions and I won't go into further
    details here). In fact, the second rule is obviously inconsistent to human
    intuition: If speed is high and distance is short, then one should brake sharply
    to stop, which is itself a fuzzy rule.

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