Consistency of fuzzy rules

From: Yaochu Jin (ftrjin@mail.ipm.net)
Date: Thu Oct 04 2001 - 07:15:26 MET DST

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    Hi,

    This might be an issue of consistency of fuzzy rules. Roughly, two fuzzy rules
    mare inconsistent in the following situations

    i) The same condition, completely different consequents
    e.g.

    R1: If x1 is A1 and x2 is A2, then y is Positive Large
    R2: If x1 is A1 and x2 is A2, then y is Negative Large
     
    ii) Although the consitions are seeming different, but the same in physical
    meanings, and the consequents are totally different

    R1: If x1 is A1 and x2 is A2, then y is Positive Large
    R2: If x1 is A1 and x3 is A3, then y is Negative Large

    Although "x2 is A2" and "x3 is A3" appears to be different conditions, they
    might imply the same situation in some cases, such as in a chemical reactor:
    "If temperature is high" may imply "conversion rate is high"

    iii) Contradictory conditions
    e.g. "The sun is bright and the rain is heavy"

    iv) Contradictory consequents
    e.g. If x is A then y is B and z is C
    However, y is B and z is C cannot happen together

    One method to avoid generating inconsistent fuzzy rules from data has been
    discussed

    "Y. Jin et el", On generating flexible, complete, consistent and compact fuzzy
    rules from data using ES. IEEE Trans. SMC-B, 29(4), 1999

    Regards,
    Yaochu

    >Date: Mon, 24 Sep 2001 18:16:21 +0200 (MET DST)
    >Originator: fuzzy-mail@dbai.tuwien.ac.at
    >From: "Weiz" <weiz@sympac.com.au>
    >To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    >Subject: Re: no title
    >X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas
    >X-Comment: Fuzzy Distribution List
    >Content-Transfer-Encoding: 7bit
    >
    >sure it is.
    >
    >Although it goes more like If Sunlight is bright AND rainfall is high THEN
    >Plant growth is rapid.
    >
    >Bright is a fuzzy set in the universe of Sunlight. (there might also be dim
    >and shaded etc) these names of course are assigned to parts of the scale of
    >brightness.Ditto for rainfall and plant growth.
    >
    >Anyway the extent to which sunlight is bright ( I.e. the membership value of
    >a particular bright value in the bright fuzzy set ) and rainfall is high
    >help shape the rapid plant growth fuzzy set from which is de-fuzzied a crisp
    >solution for the growth rate.
    >
    >Many Antecedents add to the shaping process, depending on the way one is
    >forming the shape of the output set (from which is derived the final answer
    >space) some of the Antecedents end up having no effect.
    >
    >
    >
    >
    >-----Original Message-----
    >From: tristan punzalan <avatar22@apexmail.com>
    >Newsgroups: comp.ai.fuzzy
    >Date: Monday, 24 September 2001 20:36
    >Subject: no title
    >
    >
    >>I am new to fuzzy logic and I do not know if it is okay to make rules
    >involving 5 inputs and one output as such:
    >>
    >> If A is X1 and B is Y1 then F is Z1
    >> If A is X2 and C is Y2 then F is Z2
    >> If A is X3 and D is Y3 then F is Z3
    >> If A is X4 and E is Y1 then F is Z4
    >>
    >>where A,B,C,D,E are inputs and F is the output.
    >>
    >>
    >>ApexMail now registers domains! www.apexmail.com
    >>
    >>
    >>
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    >
    >
    >
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    -------------------------------------------------------------------
    Yaochu Jin
    Future Technology Research
    Honda R&D Europe (D) GmbH
    Carl-Legien-Strasse 30
    63073 Offenbach/Main
    Germany

    Tel: +49 69 89011735
    Fax: +49 69 89011749
    Email: yaochu.jin@hre-ftr.f.rd.honda.co.jp
    Alias: yaochu.jin@ieee.org
    http://www.soft-computing.de/

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