Conditional Events and Fuzzy Conditional Events Viewed from a Product ProbabilitySpace Perspective

摘要

This paper first reviews the basic work in conditional event algebra. where if-then statements such as if b, then a are evaluated probabilistically by the conditional probability P(a/b) = P(ab)/p(b) and modeled algebraically by the mathematical equivalent of an interval of events AB, B'VAB = x in B : ab < x < b'vab = Bb'vab (principal ideal co-set form) for boolean algebra B of all unconditional events a,b,c, Despite many interesting properties. conditional event algebras stemming from the above approach lack a number of basic attributes necessary for developing a full extension of standard probability theory to conditional form. To address this, a new approach to conditioning is proffered, based upon a product space view. This is shown to remedy the above problems, but leads to certain computational difficulties. The extension to fuzzy conditioning is also discussed. (AN).