Optimistic Priority Weights with an Interval Comparison Matrix

AHP is proposed to give the importance grade with respect to many items. The comparison value that is the element of a comparison matirx is used to be crisp, however, it is easy for a decision maker to give it as an interval. The interval comparison values can reflect uncertainty due to human judgement. In this paper, the interval importance grade is obatained from an interval comparison matrix so as to include the decision maker’s judgement. An interval is determined by its center and its radius. We assume that the center is obtained by eigenvector method and the radius is obtained by interval regression analysis using the obtained centers. The interval importance grades are considered to be acceptable for a decision maker. To choose the crisp importance grades and the crisp efficinency in the decision maker’s judgement, we use DEA, which is an evaluation method from the optimistic viewpoint with respect to many input and output items. The weight in DEA and the importance grade through AHP are similar and we normalize data in order to make the weight itself in DEA represent the importance grade in AHP.