# Re: fuzzy relations between non-well founded sets?

Carlos Gershenson (carlos@jlagunez.iquimica.unam.mx)
Fri, 15 Jan 1999 20:32:21 +0100 (MET)

Hi all

well, you can find something similar at
http://jlagunez.iquimica.unam.mx/~carlos/mdl/

It is a logic that allows more than one value (fuzzy) of truthness to be
premises, and find a projection in fuzzy logic, among other things.

Cheers,
Carlos

On Mon, 11 Jan 1999, Stephen Paul King wrote:

> Hi all,
>
> I have found the following:
>
> >7.2.1.2. Fuzzy Hypersets (*)
>
> > Although fuzzy sets are now commonplace in artificial intelligence, so far as I know fuzzy hypersets have never before been
> >discussed. Fortunately, therewould appear to be no particular problems involved with this useful idea: the basic mathematics of
> >fuzzy hypersets, at least as far as I have worked it out, is completely straightforward.
>
> > The simplest example of a fuzzy hyperset is the set x defined by:
>
> > dx(x) = c,
>
> > dx(y)=0 for y not equal to x.
>
> >Here, if c=0, one has an ordinary well-founded set, namely the empty set. If c=1, one has the set x={x}. Otherwise, one has
> >something inbetween the empty set and x={x}.
>
> > Each fuzzy hyperset is characterized by a fuzzy apg, which is exactly like an apg except that each link of the graph has a
> >certain number in [0,1] associated with it. The Fuzzy AFA then states that each fuzzy apg corresponds to a unique fuzzy set. It is
> >easy to see that the natural analogue of the Solution Lemma holds for fuzzy hypersets. And, of course, the consistency of fuzzy
> >hypersets with the axioms of set theory (besides the axiom of reducibility) follows trivially from the fact that each fuzzy hyperset
> >is, in fact, a hyperset under AFA.
>
> in:
> http://goertzel.org/ben/chlog3.html
>
> Now I am wondering if we could use Kosko's mutual entropy formalism to
> think about relations between streams. Any ideas?
>
> Later,
>
> Stephen Paul King
>
> https://members-central.home.net/stephenk1/Outlaw/Outlaw.html
>
> spking1@mindspring.com (Stephen Paul King) wrote:
>
> >Has any work been done on fuzzy subsethood relations between (and/or
> >within) non-wellfounded sets?
> >Thanks,
> >
> >Stephen Paul King
>
>
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"All things are what each one thinks about them."
-Metrodorus of Kio.

Carlos Gershenson
http://132.248.11.4/~carlos/

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