Reconsideration of Numerical Comparisons in Interval Analytic Hierarchy Process

In multi-criteria decision aiding (MDCA), the alternatives are assessed concerning multiple criteria. Deriving decision makers' thinking without their burden is essential in solving her decision problem. A pairwise comparison technique helps a decision maker to quantify her intuitive and uncertain preferences. While it is easy to compare a pair of elements linguistically without caring for the other elements, the intuitively given comparisons of all pairs are rarely perfect. In other words, the evaluations in the decision maker's mind are often imprecise. This study proposes the model to obtain evaluations of the elements from the intuitively given linguistic comparisons of all pairs of elements. We consider two factors: one is inconsistency among the comparisons, and the other is the list of numbers used to replace linguistic comparisons with numerical comparisons. Based on Interval AHP, where the evaluations are intervals with some ranges, the inconsistency is reflected in the ranges, which, in other words, represents the fuzziness of a decision maker's intuitive judgment. In addition, the range makes room to modify the fixed numbers used for numerical comparisons, which are evenly ordered five integers. The modified numerical comparisons are based on the relative relations of the given linguistic comparisons. They can represent suitably her linguistic comparison sense. The proposed model consists of two linear programming problems and is used to quantify a decision maker's intuitive preference for multiple elements.