Interval weights in AHP by linear and quadratic programming

Analytic hierarchy process (AHP) is proposed to give priority weights with respect to many items. The priority weights are obtained from the comparison matrix whose elements are given by a decision maker as crisp numbers. We assume that the item's weights are intervals, because a comparison matrix based on human intuition must be inconsistent. Three models depending on the objective functions are proposed in this paper. In each model, the interval weights are determined so as to include the given comparisons. This concept is similar to the upper approximation in interval regression analysis.