Optimistic and pessimistic evaluations in interval AHP

Abstract

Analytic Hierarchy Process (AHP) is proposed to give priority weights with respect to many alternatives with many criteria. In the conventional AHP, local weights of alternatives under each criterion are obtained from the pairwise comparisons given by a decision maker. By extending the weights from crisp to interval to reflect inconsistency of the given comparisons, Interval AHP has been proposed. The global weight of an alternative is assumed as the weighted sum of local weights. The weights represent importance of criteria in evaluation so that they can be determined for each alternative from various viewpoints. We propose the interval global weights whose bounds are from the optimistic and pessimistic evaluations. Although their widths represent the possibilities of global weights, too large width from too optimistic and/or pessimistic evaluations can not be a meaningful for a final decision. Then, the obtained interval global weight should be normalized relatively so as to reduce redundancy.