# A|B vs B|A

Ellen Hisdal (ellen@ifi.uio.no)
Tue, 12 Mar 1996 14:01:19 +0100

> Date: Fri, 8 Mar 1996 22:48:59 +0100
> Originator: fuzzy-mail@dbai.tuwien.ac.at
> Sender: fuzzy-mail@dbai.tuwien.ac.at
> Precedence: bulk
> From: tvk@info.fundp.ac.be (vu khac tri)
> X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas
> X-Comment: Fuzzy Distribution List
>
> I have some problems following:
> 1. How to calcul and interpret in the form "fuzzy", "possibility" if we have the evenements probabilist?
> For example: A+ A-
> ---|--------|---------|
> B+ | 10 | 50 |
> ---|--------|---------|
> B- | 100 | 90 |
> ---|--------|---------|
> That mines: P(B+|A+) = 10/110 = 0.09 ect.,
>
> 2. How to calcul Poss(A| B and C and ....)?
> Thank you,
> Email to tvk@info.fundp.ac.be
> Best regards.
> VU KHAC TRI.

According to the TEE model for grades of membership
(see Fuzzy Sets Systems vol 25, pp. 325-348, March 1988)
the possibility or grade of membership
mu (B) (where, e.g. A=tall = element of a complete and
A nonredundant set of labels)

and B=180cm=element of a height universe)

should be interpreted roughly as P(A|B)=probability of assignment of
the label A to a person of height B.

>From the theory of probability we then have

P(A,B)=P(A)P(B|A)=P(B)(A|B)

where P(A)=sum of P(A,B) over all elements of the B universe,
where P(B)=sum of P(A,B) over all elements of the A universe.

Your two universes consist of two elements each, {A+, A-}
{B+, B-}.
The above formulas are then valid for A=either A+ or A-
and similarly for B.

Greetings,
Ellen Hisdal