Algebraic Representations of Linguistic and Numerical Modifications ofProbability Statements and Inferences Based on a Product Space Construction

摘要

This paper addresses the problem of obtaining for any given probability space (A,B, P) an extension to a probability space (Ao, Bo, Po) such that for any given function f:(O,1)n to (0,1), suitably analytic, and any given finite collection of ordinary events a, b, c,...,m in sample space B, with possible relations among them, there is an event alpha sub f = alpha sub f (a,b,c,...,m) in Bo (not dependent upon P) such that for all possible choices of P and a, b, c,...,m, Po(alpha sub f) = f(P(a), P(b), P(c), ..., P(m)) provided the right-hand side is well-defined relative to f. It is seen that the above procedure generalizes that of the problem of constructing 'conditional event algebras' relative to all conditional probabilities. Applications to problems on data fusion and combination of evidence are also provided.