A method based on bivariate almost stochastic dominance for multiple criteria group decision making with probabilistic dual hesitant fuzzy information

Probabilistic dual hesitant fuzzy sets (PDHFSs) are sound information granules to describe decision maker's aleatory and epistemic uncertainty in multiple criteria group decision making (MCGDM) process. In this paper, a bivariate almost stochastic dominance-based PROMETHEE-II method is presented to solve probabilistic dual hesitant fuzzy MCGDM problems which consider correlation averse behavior of decision makers. First, probabilistic dual hesitant fuzzy power Bonferroni mean (PDHFPBM) operator and probabilistic dual hesitant fuzzy power geometric Bonferroni mean (PDHFPGBM) operator are proposed to acquire collective preference information of decision makers. Second, based on the defined bivariate almost stochastic dominance (BASD) and BASD degree, qualitative and quantitative relationships between two probabilistic dual hesitant fuzzy elements (PDHFEs) with corresponding to all criteria are obtained. Third, distance-based correlation coefficient method for computing combined weight with respect to all criteria is proposed. Finally, a BASD-based PROMETHEE-II method is developed to determine the ranking results. Three illustrative examples followed by comparative analysis are included to show the practicality and effectiveness of the proposed method.