In a recent message, I stated that the maximum entropy principle is not applicable when the side-conditions are imprecise. Here is a concrete example. Let X be a real-valued random variable. What we know about the probability distribution ,P, is that its mean is approximaately a and its variance is approximately b, where "approximately a" and "approximately b" are fuzzy numbers defined by their membership functions. The question is: What is the entropy-maximizing P ? In a more general version, what we know are approximate values of the first n moments of P. Can anyone point to a discussion of this issue in the literature?
-- 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)
