Hitoshi Kitada (hitoshi@kitada.com)
Sun, 9 May 1999 11:55:47 +0900
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<pmd@maths.uq.edu.au>]
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> Date: Sun, 9 May 1999 12:39:15 +1000 (EST)
> From: Phil Diamond <pmd@maths.uq.edu.au>
> To: "Stephen P. King" <stephenk1@home.com>
> cc: John Wilkins <wilkins@wehi.edu.au>, Time List <time@kitada.com>
> Subject: Re: degeneracy of distributivity
> In-Reply-To: <3732F5CC.3EB3F706@home.com>
> Message-ID: <Pine.GSO.3.95.990509122601.600Z-100000@sinai.maths.uq.edu.au>
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> On Fri, 7 May 1999, Stephen P. King wrote:
>
> > Dear Phil,
> >
> > I think that it is what I am talking about! :) This degeneracy of
> > distributivity is what I thinking about. ;) I am thinking that the
> > dificulty may be dealt with in a practical sense by showing that
> > computations of asymptotic approximations to a norm (which is some sort
> > of limit -> oo) are possible for some classes of finite state systems
> > (involving bisimulation).
> > Has any study been done on the nature of this "normally distributed
> > vector"? Is is complex in the Chiatin sense?
> > http://www.cs.auckland.ac.nz/CDMTCS/chaitin/max.html (equating the
> > vector to a bit string)
> >
>
> Not to my knowledge - essentially the result follows from the degeneracy
> of the normal in a Banach space of functions.
>
> I also found: http://www.mathe.tu-freiberg.de/math/publ/pre/95_12/
> > which is apparently (from the abstract) dealing with this question! :)
>
> Ralf Korner's result is different - there is no assumption of what
> distribution the random sets have. See also Diamond & Korner "Extended
> fuzzy linear models and least squares estimates", Computers Math.
> Applic. 33 (1997), 15-32.
>
> >
> > Would you happen to have poscript or TeX e-versions of these papers? I
> > will try to order the book...
> >
>
> The book was our attempt to put a lot of fuzzy concepts on a systematic
> and rigorous basis and brings together in a book a lot of scattered
> results in papers. The basis of much of it is the link between usc fuzzy
> convex fuzzy sets and certain function spaces. This is really a basis for
> mathematical analysis using these objects and is a far cry from many of
> the applications that are being used on computers.
>
> The paper files are 12 years old and no longer Amstex because of so many
> font changes and system changes that our network has undergone. You would
> be better off (& much easier for me) to get them on interlibrary loan if
> your uni library does not have them.
>
> cordially, phil
>
>
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