Re: Neuro-Fuzzy with categorical input?

From: Jonathan G. Campbell (jg.campbell@qub.ac.uk)
Date: Thu Jul 05 2001 - 11:25:50 MET DST

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    Stefanie Koester wrote:
    >
    > Hi!
    >
    > I'd like to use a neuro-fuzzy method on the classification of data.
    > Unfortunately, the input values are both rational and nominal. Can
    > categorical input be handeled by neuro-fuzzy classification methods,
    > i.e. by introducing dummy variables? Where can I find some literature on
    > this subject? I would appreciate your help very much,

    I wonder if you are thinking of a fairly classical fuzzy rule-base
    system: i.e. fuzzifier, fuzzy rule-base, defuzzifier, where fuzzy
    rule-base is a (possibly fuzzy) relation between fuzzy sets defined on
    the input universe and fuzzy sets defined on the output universe, i.e.
    source of the relation is a set of fuzzy sets and the target is another
    set of fuzzy sets.

    If this is the case, and the inputs are defined by at least ordinal
    quantities, the source fuzzy sets are normally overlapping.

    However, if one input value (say one dimension of many) is nominal, it
    seems to me that the lack of order in values in that dimension may be
    expressed (not expressed) by ensuring that the set of fuzzy sets on that
    dimension are defined using singleton (delta function) (or
    no-overlapping rectangular function) fuzzy sets. Such membership
    functions may be combined (in fuzzy cartesian products) with
    overlapping/graded membership functions. So long as there is no overlap
    in membership functions, no order is expressed (I think?).

    [However, thinking aloud, say we have, of p input dimensions, one
    nominal dimension with a set of L values, then the resultant system will
    decompose into Q fuzzy systems defined on the remaining p-1 inputs]. In
    the past, I have written something fairly naive on this topic --
    claiming to have discovered even more universality of fuzzy rule-base
    systems! If you wish, I may be able to find it.

    Incidentally, by rational, maybe you mean 'real'? By 'ordinal' I mean
    values on which an order is defined, i.e. commonly integer or real. As
    for nominal, I take that to mean 'purely label'.

    Best regards,

    Jon C.

    -- 
    Jonathan G Campbell, Computer Science, Queen's University
    Belfast, BT7 1NN Tel +44 (0)28 90 274623 jg.campbell@qub.ac.uk
    http://www.cs.qub.ac.uk/~J.Campbell/
    

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