# [FOM] Expressive Power of Natural Languages/ Kadvany

Lotfi A. Zadeh zadeh at eecs.berkeley.edu
Fri Dec 9 19:57:14 EST 2011

```Dear John,

Thank you very much for drawing attention to the work of Kahneman
and Tversky, and to the work of Lichtenstein and Slovic. It is of
interest to observe that the works which you cited are important
contributions to decision-making under uncertainty. However, they do not
have the capability to deal with computational problems in which
probabilities and events are imprecise, as they are in most realistic
settings. In everyday settings, imprecise probabilities and events are
frequently described in a natural language, e.g., likely, very unlikely,
high, low, etc. As a simple illustration, consider the following
problem. A and B are boxes, each containing twenty black and white
balls. A ball is drawn from a box at random. In the case of A, if I draw
a white ball I win ten dollars, and if I draw a black ball I lose five
dollars. In the case of B, if I draw a white ball I win twenty dollars,
and if I draw a black ball I lose ten dollars. I am shown boxes A and B
for a few seconds, not long enough to count the number of balls. Assume
that my perception is that there are approximately fifteen white balls
in A, and approximately twelve white balls in B. I am free to choose the
box from which to draw a ball. Which box should I choose? In this
problem, the probabilities are perception-based and hence imprecise. In
many realistic settings, the same applies to gains and loses. So far as
I know, this simple problem is beyond the reach of any theory of
decision-making. Recently, Professor Rafik Aliev, Azerbaijan University,
has generalized the prospect theory of Kahneman and Tversky, and
developed methods for dealing with the posed problem. Note that the
posed problem falls within the class of CNL problems--computational
problems which are stated in a natural language. As stated in my
message, I believe that CNL problems cannot be dealt with through the
use of concepts and techniques drawn from traditional mathematics,
including probability theory.

Regards to all,

Lotfi

--
Lotfi A. Zadeh
Professor in the Graduate School
Director, Berkeley Initiative in Soft Computing (BISC)

Address:
729 Soda Hall #1776
Computer Science Division
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University of California
Berkeley, CA 94720-1776
zadeh at eecs.berkeley.edu
Tel.(office): (510) 642-4959
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