One thing missing here. The relation Rij is not merely the intersection
of Ai and Bj, but must be a fuzzy implication. There are a number of
possibilities, one being the Kleene-Dienes implication
max((1-mAi(x)), mBj(u))
These implications have different properties; one useful reference
describing these differences is
D. Park, Z. Cao, A. Kandel, "Investigations on the Applicability of
Fuzzy Inference," Fuzzy Sets and Systems, Vol. 49, pp. 151-169, 1992.
>
> Now (in the correct interpretation), we have an input x'; this is
> fuzzified -- in general to a fuzzy set A' on X (mA'(x)).
>
> Now to generate a fuzzy set on U, we compose:
>
> mA'(x)oRij(x,u) -> B'(u)
>
> This is done 'sup-star'.
>
> However, usually, mA'(.) is created as a 'singleton' set, i.e. mA'(x) =
> 1, x=x'; mA'(x)=0, otherwise. This allows much simplification to (2), in
> particular, we simply pick out one row of Rij(.,.).
>
> My confusion was that my _incorrect_ model (based on my software
> implementation -- which works okay) was as follows:
>
> - fuzzification = determination of membership of x' in the various
> Ai(.)s.
>
> - rule-base = mappings between Ais and
> Bjs.
>
> Actually, this model is adequate in many cases -- but it's different
> from the commonly agreed one.
>
> Apologies -- especially to those to whom I've spread this confusion! In
> due course, I'll be correcting parts of reports on my website. [If
> anyone wants further repentance, or wants to comment, I'd be happy to
> discuss further, either here or by private email].
>
> Best regards,
>
> Jon Campbell
>
> --
> Jonathan G Campbell Univ. Ulster Magee College Derry BT48 7JL N. Ireland
> +44 1504 375367 JG.Campbell@ulst.ac.uk http://www.infm.ulst.ac.uk/~jgc/
>
> Sent via Deja.com http://www.deja.com/
> Share what you know. Learn what you don't.
-- *********************************************************************** * * * * Scott Dick * * * Research Assistant * Cool & brilliant thought * * USF Computer Science * still under contruction * * dick@morden.csee.usf.edu * * * * * ***********************************************************************
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