A Probabilistic Hesitant Fuzzy Multi-criteria Group Decision-Making Method Integrated DIBR and Tri-reference Point Theory

As an effective tool to show the fuzziness of qualitative information, the probabilistic hesitant fuzzy set (PHFS) can utilize a group of membership degrees with a clear probability distribution to show the opinions of decision-maker (DM). Given this merit, many probabilistic hesitant fuzzy multi-criteria group decision-making (PHF-MCGDM) methods have been designed. However, most of the existing PHF-MCGDM methods have some limitations, including the difficulty of reflecting DMs' ambiguous and hesitant preferences for criteria weights and the inability to comprehensively show the impacts of DMs' irrational behaviors. To address these limitations, this paper develops a novel PHF-MCGDM method that integrates the defining interrelationships between ranked criteria (DIBR) approach and tri-reference point (TRP) theory. First, the PHF-DIBR approach is constructed to determine criteria weights by fully expressing DMs' ambiguous and hesitant preferences for the importance of criteria. Second, the novel probabilistic hesitant fuzzy correlation coefficient (NPHFCC) is developed for deriving the weights of DMs, which remedies the flaws of the existing correlation coefficients (CC). Moreover, TRP theory is used to describe the psychological behavior effects of DMs and derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about office flooring material selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness.