A consensus model for group decision making under additive reciprocal matrices with flexibility

Abstract A consensus model is proposed for group decision making (GDM) with additive reciprocal preference relations based on the technique for order preference by similarity to an ideal solution (TOPSIS). The initial positions of decision makers are expressed as additive reciprocal matrices. A method of obtaining a collective ideal additive reciprocal matrix is proposed in terms of individual ones. A novel fitness function is constructed through a linear combination of two objective functions involving the consensus degree within the group of experts and the consistency measure of individual preference relations. A new algorithm based on particle swarm optimization (PSO) is proposed to model the dynamic and iterative consensus process of GDM with flexibility. Numerical results are reported to illustrate the proposed model through some comparisons with the existing ones. The weight variance is proposed to characterize the dispersion degree of the weights of alternatives, and analyzed by considering the effects of the flexibility degree and the constraint conditions. The observations reveal that with an increasing of the flexibility degree, the dominant alterative may be chosen, or any solution may not be reached by a group of experts.