An Approximation to the Value Efficient Set

In this paper we assume a decision making situation under certainty with incomplete information on the decision maker’s preferences, by means of a vector value function defined on the consequence space. From that function we consider an additive value representation with partial information on the scaling constants defined by polyhedral cone and the concept of value efficient set. We introduce an approximation set whose generation may be easier than the one of the value efficient set. Nesting properties based on the interactive reduction of the uncertainty about the scaling constants, which provide more precise vector value functions, lead to better approximations. Finally, we propose an interactive algorithm based on the approximation set and two examples illustrating the method.