Measurement Theory and Decision Aid

When facing a decision problem, the first thing to do is to structure this problem, to create a model of the problem in order to be possible to apply to this model a systematic treatment. The elaboration of such a systematic treatment (decision aid method) depends on the model but also on the information obtainable from the decision-maker. As the decision aid methods are often based on the notion of real number, it is fundamental, given a set X and some information about this set, to know 1)when it is possible to assign to each element x of X a real number µ(x) SO that, by specifying how to use these numbers, they can represent the information given on X (representation problem);2)what kinds of mathematical manipulations are possible with these numbers, that is what statements can be meaningfully made using these numbers (problem of meaningfulness).