Dear Rich, Your interesting question stirred a lively discussion. Your question raised another question: Is the conceptual structure of probability theory an appropriate framework for formulating a definitive answer to your question? In my view, the answer is: No.
The problem is: probability theory does not differentiate between fuzziness and randomness or, concomitantly, between possibility and probability. Here is a simple example. I meet Valentina. I do not know how old she is. My perception is that she is about 40. In this instance, Valentina's age is a fuzzy variable and "about 40: is its fuzzy value. Next, suppose I am staying at a hotel and ask the doorman: How long will it take to get to the airport by taxi? His answer is: usually about thirty minutes. In this instance, travel time is a random variable. About thirty minutes is a fuzzy event, and usually is a fuzzy probability of this event. Combinations of fuzzy variables and random variables are governed by different rules. As an illustration, suppose that I ask myself: If I leave the hotel at about 10 and usually it takes about thirty minutes to get to the airport, at what time will I arrive there? Try to answer this question using standard probability theory. A fuller discussion of fuzziness and randomness may be found in my paper, "Toward a generalized theory of uncertainty (GTU)—an outline," Information Sciences, Elsevier, Vol. 172, 1-40, 2005. Warm regards to all, Lotfi -- Lotfi A. Zadeh Professor in the Graduate School Director, Berkeley Initiative in Soft Computing (BISC) _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
