Thank you for mailing this paper on your mailing list (Lotfi suggest me
that).
Dear Lotfi,
The problem you raise (part of the many fundamental contributions you
brought to the domain), aims in enlarging the formalism of subjective
probabilities in order that it cope with the usual way of thinking in
uncertainty. To "humanize" probability theory, amounts to create models
which reproduce as much as possible the "input-output" of human mind,
without breaking off communication with the classical theories from
which they emerge.
As you mention, the difficulties of creating such models arise because
of the imprecision of our perceptions, the imprecision of the natural
language which describes them and the complex computations necessary to
combine them. The concepts of fuziness, granularity, precisiated natural
language and computational theory of perceptions you introduced, help
solving some of these difficulties, succeeding to open the way for
further contributions. We cannot but thank you for this creative and
original impulse.
Unfortunately, the more rigorous a theory, the less it looks like the
common sense of thinking. To answer to the simple question mentioned in
the paper: "what is the probability that my car may be stolen", the man
in the street is able to provide quickly an answer which represents
approximately his opinion. The question I can't stop asking myself is:
"what is he doing in his mind during the few seconds of thinking"? One
can reply to this that a beautiful theory is not built with the poor
mechanisms of thinking of the man in the street. Perhaps, but all the
same, these poor mechanisms are rapid and efficient. If I try to analyse
what I am doing in my mind to find the answer to the above question,
this is what I find:
- First, a rapid pass in review of the arguments for my car be
stolen (set S) and of my car not be stolen (set NS);
- each proposition (representing my argument) belongs more or less to
one of these sets; I use the generalized constraint (Zadeh 1986):
X isr S
where, for example,
X = it is night (proposition or variable)
S = stolen (constraining relation)
r = 0.8 (degree in which the car could be stolen during
night
Another example: Y is NS
Y = the car is near the police house
NS = Not Stolen
q = 0.9 (the car cannot be stolen near the police)
- then, adding all the weights assigned to the propositions belonging to
S and all those belonging to NS, I can compare these two sums and have
an opinion concerning the chances of my car being stolen this night. If
I want to have numbers between 0 and 1 (to approach the known values of
probabilities), I can evaluate "proportions" of favorable and contrary
sum of weights.
In Problem 3 of the paper, the hotel clerk builts in his mind arguments
corresponding to the sets labelled, say, 20, 30 or 40 min.
The perception based information "X = no rain" will be comprised in
the set labelled 20' with a great r. A perception like "it is raining
lightly", belongs to the set labelled 30' with a great 'r' too, and the
perception based information "it rains cats and dogs" will reinforce the
set 40'. Obviously, other perception based information will reinforce
the various sets (like the kind of car which is used, the skill of the
driver, the intensity of the lighting on the road etc) providing them
more or less weight in each set. Surely, an accident on the road could
change completely these evaluations, which are only probable.
Usually, these evaluations are not numerical but qualitative, enabling
to order the sets. But numerical proportions of such weighted
perceptions could lead to numerical values comprises between 0 and 1.
Even problems of the type 6-8 (common sense reasoning) can be handled by
this technique. If Robert is young and most of young men are healthy
this is a strong argument (great 'r') toward the set labelled 'healthy'.
All the other perception based information concerning Robert's health
(preceding diseases, heredity etc) will be integrated to one of the sets
'healthy' or 'non healthy' with their corresponding value of 'r'.
Finally the 'chances' of each set result quantitatively or qualitatively
from the sum of weights.
These are my thoughts concerning a commonsense evaluation of chances
(probability,) based on perceptions. It is done by introspection, which
avoids great mathematical developments. But so are the mechanisms of
thought: simple and efficient. Do you think it is a way which can lead
to a solid model?
Friendly,
Marianne
Marianne Belis
Directrice=
Professeur d'Informatique et d'Intelligence Artificielle
Supinfo Paris - Ecole Sup=E9rieure d'Informatique (ESI) =
http://www.supinfo.com
Paris Academy Of Computer Science
23, rue de Ch=E2teau Landon - 75010 Paris
T=E9l : 01 53 35 97 00 - Fax : 01 53 35 97 01
