A decision analysis with due consideration of the non-determinacy of the interval weight

Abstract

The analytic hierarchy process (AHP) is known as a technique for multiple criteria decision analysis. Considering the vague evaluation by a decision maker, the robustness in the result of the decision analysis by AHP is required. In this study, we propose a decision analysis reflecting the vagueness of the evaluations by estimating interval weights for representing the importance of criteria and alternatives. Non-uniqueness of solutions in the estimation problem of normalized interval weight vector occurs frequently. We first show that the set of optimal solutions to the interval weight estimation problem is bounded and represented by scalar multiplications of an estimated interval weight vector. Utilizing this property, a decision analysis applying the worst case analysis to the vagueness in the interval weights and the parametric analysis to the non-determinacy caused by the non-uniqueness of the estimated interval weights is proposed. This method provides a more detailed decision analysis under the same information as the conventional AHP.