A decision making model based on intuitionistic multiplicative preference relations with approximate consistency

Intuitionistic fuzzy numbers possess the ability to model the bipolarity of practical objects and phenomena. The positive and negative opinions of decision makers (DMs) could be captured by intuitionistic multiplicative preference relations (IMPRs). In this study, the known consistency definitions of IMPRs are reviewed and the underlying ideas are analyzed. By considering the uncertainty shown by IMPRs, the concept of approximate consistency (AC) is proposed. Then the AC and acceptable AC of IMPRs are defined by dividing the non-determinacy judgements of the DM with the introduction of an attitude factor. The methods of eliciting the priorities of alternatives from an IMPR with acceptable AC are studied. A decision making model is proposed by considering the acceptable AC of IMPRs. Numerical results are reported to demonstrate that the application of different attitude factors could lead to different optimal solutions. It is observed that the inherent property of IMPRs should be incorporated into theoretical and practical models under intuitionistic fuzzy environments.