A min-max goal programming approach to priority derivation in AHP with interval judgements

We deal with the problem of priority elicitation in the analytic hierarchy process (AHP) on the basis of imprecise pair-wise comparison judgements on decision elements. We propose a min-max goal programming formulation to derive the AHP priorities in the case that the decision maker provides preference judgements in the form of interval numbers. By applying variable transformations, we formulate a linear programming model that is capable of estimating the priorities from both consistent and inconsistent interval judgements. The proposed method is illustrated by numerical examples.