Incomplete interval fuzzy preference relations for supplier selection in supply chain management

In the analytical hierarchy process (AHP), it needs the decision maker to establish a pairwise comparison matrix requires n(n-1)/2 judgments for a level with n criteria (or alternatives). In some instances, the decision maker may have to deal with the problems in which only partial information and uncertain preference relation is available. Consequently, the decision maker may provide interval fuzzy preference relation with incomplete information. In this paper, we focus our attention on the investigation of incomplete interval fuzzy preference relation. We first extend a characterization to the interval fuzzy preference relation which is based on the additive transitivity property. Using the characterization, we propose a method to construct interval additive consistent fuzzy preference relations from a set of n-1 preference data. The study reveals that the proposed method can not only alleviate the comparisons, but also ensure interval preference relations with the additive consistent property. We also develop a novel procedure to deal with the analytic hierarchy problem for group decision making with incomplete interval fuzzy preference relations. Finally, a numerical example is illustrated and a supplier selection case in supply chain management is investigated using the proposed method.