Consistency Improvement-Driven Decision-Making Methods with Probabilistic Multiplicative Preference Relations

The hesitant multiplicative elements (HMEs) are useful tool to address situations in which the decision makers (DMs) are hesitant about several possible multiplicative values. However, the occurring probabilities of the elements in the HME are equal, which is obviously unpractical. To cope with this issue, this paper introduces the concept of probabilistic multiplicative preference relations (PMPRs), in which the occurring possibilities of the elements are considered in probabilistic multiplicative elements (PMEs). Then, several additional concepts are presented, including order consistent PMPRs and consistent PMPRs. A linear optimization model is established to generate the optimal deviation values, which is followed by an approach for constructing consistent PMPRs. For the unacceptable consistent PMPRs, two decision-making methods are further designed to improve their consistency until the adjusted PMPRs are acceptable, including automatic iterative decision-making algorithm and interactive decision-making algorithm. Finally, a numerical example of selecting the desirable supplier is provided, and the comparison with existing approaches is performed to validate the rationality and effectiveness of the proposed algorithms.