An integrated method for multi-granular probabilistic linguistic multiple attribute decision-making with prospect theory

Multi-granular fuzzy linguistic modeling enables evaluators to express opinions with several linguistic term sets, but it cannot simultaneously reflect hesitancy and preference degrees of decision makers (DMs). To solve this issue, we introduce probabilistic linguistic term sets (PLTSs) and investigate multi-granular probabilistic linguistic (MGPL) modeling. We first redescribe the multiplication and exponentiation of PLTSs by using the sign function to enhance their universality and generalization. Since multi-input arguments are interrelated and DMs have different psychological cognition, we then define prospect probabilistic linguistic Muirhead mean (PPLMM) operator and prospect probabilistic linguistic weighted Muirhead mean (PPLWMM) operator to fuse MGPL information (MGPLI). Moreover, we improve prospect theory (PT) based on PLTSs' new operational laws (i.e., multiplication and exponentiation) and extend it to MGPLI environment. Finally, an integrated multi-granular probabilistic linguistic modeling based on proposed PT and PPLWMM operator is constructed and applied to solve probabilistic linguistic multiple attribute decision-making problems.