Incomplete Large-Dimensional Pairwise Comparison Matrices

Abstract

This chapter is concerned with large-dimensional pairwise comparison problems and answers the following research question: “How can the amount of preference information required from the decision maker in a large-dimensional pairwise comparison matrix be reduced while still obtaining comparable priorities of objects?” The chapter reviews a real-life case-study motivating the need for methods dealing with large-dimensional pairwise comparison problems and discusses desirable properties of methods for constructing an incomplete pairwise comparison matrix and deriving priorities of objects. A two-phase method ensuring the desirable properties is introduced in detail, and its application to a real-life case study is described. The excellent performance of the method in terms of saving a large number of pairwise comparisons required from the decision maker and obtaining comparable priorities of objects is supported by simulations. In addition, the method is critically compared with another well-known method for constructing incomplete pairwise comparison matrices.