A decision-making model with sequential incomplete additive pairwise comparisons

Abstract A sequential modelling of pairwise comparisons exhibits the capability to effectively cope with some complexity in a decision making process. When the complexity of decision making problems leads to incomplete pairwise comparisons, a feasible approach to optimal solutions is worth investigations. In this paper, we propose the idea that a missing value is mainly dependent on the neighbour ones in a sequential of comparisons; and develop a decision making model. First, additive pairwise comparisons with missing values are captured by proposing a sequential model and some properties are studied. Second, an optimization model for completing an incomplete additive reciprocal matrix (ARM) is recalled. Based on the sequential model, the missing values of incomplete ARMs are estimated using particle swarm optimization (PSO). Different with the previous studies, the permutations of alternatives are considered to give various estimations of a missing value. Third, a granularity-based method is proposed to improve additive consistency of a completed ARM; and the best granularity level is chosen. Finally, a decision-making algorithm is established, where the opinions of decision makers (DMs) are expressed as incomplete ARMs. Some cases are studied to illustrate the finding that multi-optimal solutions could exist in a decision making problem. The novel phenomenon is in agreement with the case that different orders of comparing alternatives may yield different results due to the inconsistency of human-originated information.