Dear David:
Thank you for your constructive comments.
For your information, there is an extensive literature on the
relationship between fuzzy logic and probability theory, going back to a
paper by Loginov in 1966. The most thoroughly studied aspect of this
relationship relates to the connection between fuzzy sets and random
sets. (See the book by Irvin Goodman and Hung Nguyen (1985) Uncertain
Models for Knowledge-Based Systems, Amsterdam: North Holland.) A
discussion of the relationship between fuzzy logic and probability
theory may be found in my paper entitled "Probability Theory and Fuzzy
Logic Are Complementary Rather Than Competitive," published in
Technometrics, Vol. 37, No. 3, pp. 271-276, 1995. My current view, which
is more radical than that expressed in the cited paper is that
probability theory should be based on fuzzy logic rather than on
bivalent logic.
You suggest that standard Bayesian techniques can deal with
partiality of truth. Could you show me, in concrete terms, how such
techniques can be applied to the solution of problems stated in my
message of November 11. For convenience, three of the problems are
reproduced below.
1. The tall Swedes problem: Most Swedes are tall. What is the
average height of Swedes?
2. Usually it is not very cold, and usually it is not very hot in
Berkeley. What is the average temperature in Berkeley?
3. The balls-in-box problem: A box contains about 20 black and
white balls. Most are black. There are several times as many
black balls as white balls. What is the probability that a ball
drawn at random is white?
Please note that I would like to see concrete solutions rather than
general statements. I believe that you will come to the realization that
the relationship between fuzzy logic and probability theory is no way
as simple as one may think.
Cordial regards,
Lotfi
- --
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)
Address:
Computer Science Division
University of California
Berkeley, CA 94720-1776
Tel(office): (510) 642-4959 Fax(office): (510) 642-1712
Tel(home): (510) 526-2569
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http://www.cs.berkeley.edu/~zadeh/
