A generalized TODIM approach based on information measurement and consensus building model in probabilistic hesitant fuzzy environment

Information measurement and decision-making methods are two important aspects in the application of probabilistic hesitant fuzzy elements (PHFEs), and these issues are crucial for improving decision quality and enhancing the applicability of PHFSs. This paper focuses on the entropy measure and score function of PHFEs, and then proposes a generalized TOIDM method based on information measurement and consensus building. In this contribution, we develop a novel non-probabilistic entropy measure by two non-fuzzy elements and a novel score function based on sigmoid function. The novel non-probabilistic entropy of PHFEs can comprehensively reflect the dynamic changes of fuzzy uncertainty and hesitant uncertainty, and provide a new axiomatic framework. The novel score function of PHFEs can synthesize multiple information effectively with strong integrity. In the sequel, the two proposed information measurement methods are compared with existing methods to further verify the validity of the developed methods. Eventually, a consensus building model is constructed based on the proposed information measurement method, and then a generalized TODIM approach based on information measurement and consensus building is proposed for probabilistic hesitant fuzzy environment. The developed approach is demonstrated with an emergency rescue planning decision-making problem. Sensitivity analysis and comparative analysis are employed to verify the validity and stability of the approach and information measures proposed in this paper. Based on the findings of this study, we conclude that the proposed methods effectively enrich the existing information measurement methods and decision-making methods in the field of probabilistic hesitant fuzzy.