On subjective programming in multi-criterion decision making

In multi-criteria decision making, the best alternative is usually selected from a number of alternatives as the one that gives the best effect with respect to the preference of the decision maker. In 1964, Aumann published the first results available on programming based upon the subjective judgment of the decision maker, which he named subjective programming. Following his work, in this paper, some duality theorems for subjective programming with additive (linear) and incomplete preferences are derived by defining vector-valued Lagrangian with its geometrical interpretation.