Distance-based consensus reaching process for group decision making with intuitionistic multiplicative preference relations

The intuitionistic multiplicative preference relation uses Saaty’s 1∕9-9 scale to depict people’s opinions from the prior and not prior aspects. Due to its objectivity in representing people’s cognition, the intuitionistic multiplicative preference relation has attracted extensive attentions of scholars. In this paper, we study the distance-based consensus measures in the context of group decision-making with intuitionistic multiplicative preference relations. First of all, some new distance measures between intuitionistic multiplicative numbers/sets are proposed, which contains the improved Hamming distance, the improved Euclidean distance, and their weighted forms. Then, we investigate their desirable properties. To aid the group decision-making process, we further develop a new consensus measures regarding intuitionistic multiplicative preference relations based on the proposed distance measures. Afterwards, a new group decision-making method is proposed to solve the complex group decision-making problems with intuitionistic multiplicative preference relations. Finally, an example concerning the project investment selection is given to demonstrate the proposed group decision-making method, and then we compare the proposed method with other existing group decision-making methods with intuitionistic multiplicative preference relations in detail.