Re: Fuzzy vs. Probability: Just give it to me in plain English

Mon, 20 May 1996 12:12:49 +0200

Things are not as simple as that. You might devise an experiment to find if
Bill Clinton is 'tall' - just ask everyone if he is, find that 28% of
American citizens think so, and name him '0.28 tall'. You may even find the
probability that a man who was called 'tall' by a random UCLA graduate is over
1.80 . I think it is meaningless.
Fuzziness is not a collection of yes/no questions. It is the fact that height
is not a strict formula, even if you ask one person. Is a 1.76m man tall ? I
don't know! He is taller then I am. I might call him 0.45 tall, which only
indicates that he is shorter than 0.57m tall man.
The thing is, some questions are not yes/no questions. If I want to work with
them, I need fuzzy.

Probability always assume that the true answer exists somewhere, we just
don't know it. This was the example of the land/sea problem: What does it mean
to have a region which is 0.3 land ? that it is 70% of its area is sea ? or
that 30% of the reports you got about it said it was 'land' ? Or the region
is flooded 70% of the year ? or maybe it is just a big swamp ?

I think any of these interpretations can be translated to some probability
problem, but each of them is deferent. It depends on what you ask for, and
anything you do with the datum depends on what you think it means. The only
sure thing is that this are is 'less' land than a 0.32 land region.

You may try this problem: If region A is 30% land, and region B is 60% land,
how about the combined region of A and B ? it yields different results for
each interpretation.

-----------------
Piglet sidled up to Pooh from behind.
"Pooh?" he whispered.
"Yes, Piglet?"
"Nothing," said Piglet, taking Pooh's paw, "I just wanted to be sure
of you." -A.A.Milne ( thanks to Jo Ann )

-Moddy (moddy@wisdom.weizmann.ac.il)