Dear Konrad:
It is true that in some instances ambiguity and imprecision
are close in meaning, but in most instances this is not the case.
Example l: Robert asked me to meet him at 8. Did he mean 8 am or 8
pm? Here we have ambiguity but no imprecision. Example 2: Robert asked
me to meet him a few minutes before 8 am. Here we have imprecison but no
ambiguity.
You suggest interpreting " approximately X" as a probability
distribution centering on X. This is a legitimate interpretation. But
how would you deal with Version 2 using this interpretation ? (Version
2: If I choose option A ,I will get "approximately a." If I choose
optionB, I will get "approximately b" with probability " approximately
p," or "approximately c" with probability l - "approximately p," with
a lying between b and c. Which option should I choose?
I believe that in the course of trying to come up with an
answer, you will come to the realization that, contrary to conventional
wisdom, existing bivalent-logic-based decision theories break down when
imprecision is introduced. The reason, as I have pointed out in earlier
messages,is that such theories are focused on partiality of certainty,
but fail to provide tools for dealing with partiality of truth,
partiality of possibility and partiality of preference. What is not
recognized to the extent that it should, is that certainty, truth and
possibility are distinct concepts.
Sincerely,
Lotfi
--
Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720 -1776
Director, Berkeley Initiative in Soft Computing (BISC)
