USING A NOTION OF ACCEPTABLE IN UNCERTAIN ORDINAL DECISION MAKING

Abstract

We focus on the problem of constructing decision functions to aid in the valuation of alteratives in uncertain decision making. We discuss different types of scales available for representing the payoffs associated with the alternatives. Here we consider the case in which our basic scale is an ordinal case. Here however we augment this ordinal scale by allowing an additional notion. We indicate one special element on the scale which we call the denoted element. We name such a scale a Denoted Ordinal Scale (DOS). We point out that a DOS allows a binary partitioning of the basic ordinal scale which can be associated with differing semantics and used for various purposes. Here we focus on a binary partitioning and use a semantics which provides a classification of payoffs as to whether they are acceptable or not. This allows us to have information such as A is preferred to B but both are acceptable. We show how a DOS with this semantics can be used to construct sophisticated decision functions.