Re: fuzzy finance


Subject: Re: fuzzy finance
From: Paul Victor Birke (nonlinear@home.com)
Date: Thu Mar 02 2000 - 23:10:33 MET


"P.G.Hamer" wrote:
>
> Paul Victor Birke wrote:
>
> > <snip>
>
> > It is kinda back to the poison water bottle definition of membership
> > versus probability. While for that story it is clear, it may not be so
> > clear in other contexts, the distinction between membership and
> > probabiltiy.
>
> As an occasional lurker, the poison water example does /not/ seem
> to preclude a probabilistic model. Just model the probability that a
> panel/oracle would judge the water as poisonous.
>
> How do you know these probabilities? Sounds like the same
> sort of problem as determining membership functions.
>
> I'm not trying to convert the world to the use of probability. I do
> have a long-standing problem trying to get any sort of handle
> on fuzzy. The literature has a tendency to say that you cannot
> address some sorts of problem with probability [eg the poison
> water example]. As I believe that you can, I find this argument
> totally unconvincing. I really need to see how the performance
> of the fuzzy solution compares to that of the probabalistic one.
> Where performance can include both accuracy and computational
> simplicity. Or have the incorrectness of my belief exposed.

Very good point!! See some comment below (*)
>
> > Like I mentioned before, I look at pricing philosophically
> > in a Fuzzy Setting. Personally, I am more happier there than placed in
> > sort a roulette wheel Probability Theory Setting.
>
> As an observation, this sounds awfully like the Bayesian/frequentist
> positions in statistics.

I think this is a good point and had occurred to me as I was writing the
last part. I wonder if anything more can be made of this. Are
membership functions in any way Bayesian? Pre-knowledge as it were.
The essence of Bayesian is the conditional probability statement.
Entering a situation to judge an event with some kind of prior relevant
knowledge.

Whereas, probability does not require such prior knowledge. Just a
value based on sufficient observations.

I wonder Peter if you could take you insightful observation a bit
further.

(*) I could also agree that a comparison with numerical algorithms re
Probability vs Fuzzy as giving some kind of hint which is more powerful
or which in what context might prove more useful.

BTW Did you notice I was somewhat vague!

Paul

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