Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making

The consistency of interval multiplicative preference relations is studied and applied to group decision making. Weak transitivity for interval multiplicative preference relation is defined by comparing two interval multiplicative preferemnce values using a possibility degree formula. The consistent interval multiplicative preference relation is defined based on interval operations, which provides a convenient means to check whether an interval multiplicative preference relation is consistent. A goal-programming model is established to derive the interval priority weight vector from an interval multiplicative preference relation, which must solve only one model. An algorithm is developed through interaction with decision makers to ensure the transitivity of an interval multiplicative preference relation. The proposed methods are then extended to deal with incomplete interval multiplicative preference relations, which can determine the priority weight vector without estimating missing values. An algorithm is also developed to derive the priority vector from group multiplicative preference relations. This algorithm can help decision makers ensure the weak transitivity of their provided multiplicative preference relations.