Abstract
In this study, the fusion of probabilistic hesitant fuzzy sets (PHFSs) and rough sets is explored and applied to uncertain multi-criteria decision-making (MCDM). First, to reduce the huge amount of computation of probabilistic hesitant fuzzy operations in the MCDM process, we introduce an advanced method to obtain normalized PHFSs (NPHFSs), in which each probabilistic hesitant fuzzy element (PHFE) has the same length and probability distribution. Second, based on NPHFSs, a novel probabilistic hesitant fuzzy rough set (PHFRS) model is established to solve the information aggregation problem in MCDM. Subsequently, we propose the concept of fuzziness of a PHFRS and develop a fuzziness-based objective weight determination method. Further, we construct an extended PROMETHEE II method based on a PHFRS for MCDM problems. Finally, we analyze the effectiveness of our proposed method through two MCDM problems along with experimental comparisons. The results illustrate that the proposed method is useful in numerous uncertain application fields.
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