Group Decisions in Interval AHP Based on Interval Regression Analysis

Abstract

For encouraging communication in a group decision making, this paper proposes methods to aggregate individual preferences. The individual preferences are denoted as the interval priority weights of alternatives by Interval Analytic Hierarchy Process (Interval AHP). It is proposed to handle subjective judgments since the induced results are intervals reflecting uncertainty of given information. When each decision maker gives the judgments on alternatives, the priority weights of alternatives are obtained. In the sense of reducing communication barriers, such information helps group members to realize their own preferences and the others’ opinions. Then, they are aggregated based on the concept of the interval regression analysis with interval output data, where two inclusion relations between the estimations and the observations are assumed. From the possibility view, the least upper approximation model is determined so as to include all observations. While, from the necessity view, the greatest lower approximation model is determined so as to be included in all observations. The former possible aggregations are acceptable for each group member and the latter necessary ones are useful for the supervisor at the upper level of decision making.