Reaching consensus in group decision making with non-reciprocal pairwise comparison matrices.

In a complex group decision-making (GDM) process, decision makers (DMs) usually encounter some uncertainties. The uncertainty experienced by DMs could be characterized by the non-reciprocal property of pairwise comparisons. In this paper, the concept of non-reciprocal pairwise comparison matrices (NrPCMs) is introduced to generally capture the situation with the breaking of reciprocal property. The transformation relation between NrPCMs and interval multiplicative reciprocal matrices (IMRMs) is addressed. It is identified that NrPCMs together with IMRMs are inconsistent in nature. Then a consistency index of NrPCMs is constructed according to cosine similarity measures of two row/column vectors. An optimization-based method for eliciting priorities from NrPCMs is proposed. The properties of the proposed consistency index and prioritization method are investigated. Furthermore, a model of building consensus in GDM with NrPCMs is formed, where an optimization model is constructed and solved using a particle swarm optimization (PSO) algorithm. Some comparisons with the existing methods are reported by carrying out numerical examples. The obtained results reveal that NrPCMs provide a new yet effective way to capture the uncertainty experienced by DMs. [ABSTRACT FROM AUTHOR]