Lecture
The class of multi-criteria choice problems is very important from a practical standpoint. In such problems, not one but a whole range of factors affecting the choice are taken into account. The evaluation of each available alternative is a vector whose dimension depends on the number of factors under consideration, and to solve the DMP it is necessary to construct a scale of preferences over the available alternatives. However, since the set of multidimensional vectors is not ordered, substantial difficulties arise in constructing such preferences.
The two most common types of preferences are Pareto dominance and the lexicographic preference relation. However, despite its simplicity, the lexicographic preference relation has a significant drawback. It is not continuous, and therefore cannot be used to construct an aggregate criterion for the DMP. This criterion defines a utility or value function that assigns a certain numerical value to each vector evaluation of the DMP. The utility function, in turn, defines a preference relation on the set of admissible evaluations.
Constructing an aggregate criterion is a fairly labor-intensive task. Indifference curves play an important role here, making it possible to single out classes of evaluations that have the same value for the DM.
Comments