Green supplier selection based on probabilistic dual hesitant fuzzy sets: A process integrating best worst method and superiority and inferiority ranking

China’s equipment manufacturing industry is increasingly important due to the development of economic globalization. Selecting the proper suppliers, taking into consideration the economic and environmental benefits, is strategic due to its impacts on the operation and competitiveness of an enterprise. Uncertainty in the selection of suppliers creates challenges for managers. The probabilistic dual hesitant fuzzy sets (PDHFSs) are powerful and effective tools to handle uncertain information, which integrate the strengths of both the dual hesitant fuzzy sets and probabilistic hesitant fuzzy sets. Considering that the best worst method (BWM) is an efficient weight-determination method, which can simplify the calculation process and improve the consistency degree of the results. The superiority and inferiority ranking (SIR) integrates the strengths of most multi-criteria decision making methods in handling unquantifiable, cardinal and ordinal data. In this paper, we developed an integrated group BWM and SIR to help managers select the optimum suppliers in which the evaluation is expressed in PDHFSs. In this multi-criteria group decision making (MCGDM) problem, the BWM with PDHFSs is investigated to obtain the weights of experts and criteria. A consistency reaching method based on the input-based consistency ratio is proposed to overcome the barrier of the low consistencyrelied on the pairwise comparison and reduce the computation complexity. Furthermore, with the weights of criteria and experts acquired by the PDHFS-BWM, the SIR is extended to the probabilistic dual hesitant fuzzy information environment. A numerical example is given to verify the validity and feasibility of the proposed method, and comparison are conducted to show its advantage.