The 2-rank additive model with axiomatic design in multiple attribute decision making

Abstract

In this paper, we study the 2-rank multiple attribute decision making (MADM) problem where alternatives are divided into two preference-ordered categories. We begin our study by introducing five axioms that characterize an “ideal” 2-rank additive MADM method, and then present an impossibility theorem: Five axioms cannot be satisfied simultaneously due to the intrinsic conflict among them. Next, we propose two simple 2-rank MADM methods: Permutation-based 2-rank method (PRM) and Ranking-based 2-rank method (RRM), and explore their desired properties based on the axioms. Furthermore, we design detailed simulation experiments and find out that the PRM and the RRM share the same 2-rank result in most cases although these two methods violate different axioms. Finally, we illustrate the PRM and the RRM through a consumer preference analysis case study.