A Cone-Dominance Approach for Discrete Alternative Multiple Criteria Problems with Indifference Regions

Abstract

In this paper, we address the problem of solving discrete alternative multiple criteria decision making (MCDM) problems where some or all of the criteria might have indifference regions. We utilize the classical cone-dominance approach and significantly extend the associated theory. We then develop a convergent solution method based on cone-dominance for achieving the most preferred choice. The convergent method utilizes pairwise comparisons of the alternatives by the decision maker (DM) to eliminate inferior or dominated alternatives and to arrive at the optimum. The stated theoretical development significantly strengthens the theory of cones and presents a streamlined approach for solving the stated MCDM problems. We present a numerical example to illustrate the application of the method in finance. We also present a simulation study, evaluating the performance of the method on several hundred randomly generated test problems. Results of the simulation study are analyzed to assess the possible effects of the presence of indifference regions on the required number of pairwise comparisons to reach the optimal choice.