Stephen P. King (firstname.lastname@example.org)
Fri, 07 May 1999 10:16:44 -0400
Phil Diamond wrote:
> In comp.ai.fuzzy you write:
> > Is there a fuzzy logical version of this, e.g. the MLE and the
> >consequent definition of the Fisher Information? Also, is there a way
> >to parametrize the sharpness of the fuzzy normal distribution, perhaps
> >as a function of the \theta parameter?
> I have only come into this thread now and haven't read earlier posts.
> However, there are significant problems in even defining the normal
> distribution for fuzzy random variables. This is related to the same
> difficulty with convex compact valued random variables (NN Lyashenko,
> J. Soviet Math 21 (1983), 76-92). The only normal distribution is
> degenerate in the sense that it is a constant set (the expectation)
> translated by a normally distributed random vector. Since the level
> sets of FRV will be convex, compact sets in the mathematically
> tractable cases, the same degeneracy arises. However, since I have
> not read what others wrote, this may be entirely different from what
> you are talking about.
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
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)
I also found: http://www.mathe.tu-freiberg.de/math/publ/pre/95_12/
which is apparently (from the abstract) dealing with this question! :)
I have been trying to make sense of B. Kosko's ideas of a "information
wave equation": in chapter VII of his book Fuzzy Engineering
[http://www.prenhall.com/books/esm_0131249916.html] and comparing it to
B. Roy Frieden's resent work:
> I have a paper about MLE for fuzzy linear models based on uniformly
> distributed errors (in Springer Lecture Notes in Computer Science
> No. 313, 1988). Even here, the results are pathological and the
> estimators are second order fuzzy sets. You can find out a little
> more on fuzzy random variables in the paper "Fuzzy Kriging", FSS
> 33 (1989), 315-332. A very terse description is given in Diamond
> & Kloeden, "Metric Spaces of Fuzzy Sets", World Scientific, 1994.
Would you happen to have poscript or TeX e-versions of these papers? I
will try to order the book...
> Cordially, phil diamond
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