> Your comment touches upon a basic issue-- the semantics of > imprecision. Please note that imprecision is distinct from ambiguity.
I agree, there is a subtle difference in the meaning of these words. The problem as stated was ambiguous as it had more than one possible interpretation (in fact an infinite number of them). The cause of the ambiguity was that it was stated in an imprecise way. > If you do not like this characterization of "approximately > X," use whatever you prefer so long as it is realistic. Sure. To me it seems natural to make "the value of x is approximately X" well defined by specifying the probability density function p(x=y) describing, for all real numbers y, the strength of my belief that the value of x is equal to y. This function will have relatively large values at and near X, but its choice will also depend to a large extent on my prior knowledge of the world in general, and particularly on factors such as my knowledge of the problem at hand, the language use habits of whoever told me that x is approximately X, and the amount of trust I have in this source of information. > What you will > find is that existing bivalent-logic decision theories are ill-suited to > deal with the problem of imprecision. I disagree. After the linguistics have been taken care of, for instance by stating the problem quantitatively using fuzzy sets, probability distributions, or any other method, we are down to an inherently bivalent problem such as (in the example we are looking at) "should I buy stock A or stock B?" This is exactly the sort of question for which decision theory is well suited. > Indeed, given the fact that in > most realistic settings much of decision-relevant information is > perception-based and hence imprecise, it is hard to understand why > decision theories have lavished so much attention on decision-making > under uncertainty, and paid so little attention to the basic problem of > decision-making in an environment of imprecision and partial truth. The way I see it, imprecision and partial truth are specific forms of uncertainty. regards, Konrad
