Probabilistic Hesitant Fuzzy MEREC-TODIM Decision-Making Based on Improved Distance Measures

In the field of fuzzy sets, distance measures can effectively quantify the relevant uncertainty. Regarding hesitant fuzzy sets (HFSs), improved hesitant fuzzy distance measures have recently been proposed by fusing classical distance measures with hesitation degrees, and the corresponding information enrichment can be probabilistically advanced to pursue new distance measures of probabilistic hesitant fuzzy sets (PHFSs). Aiming at PHFSs, the improved distance measures of HFSs are simulated and extended in this paper, and thus improved distance measures of PHFSs are proposed; the new PHFSs distances are utilized to construct a new method of probabilistic hesitant fuzzy decision-making, called MEREC-TODIM. Firstly, the new probabilistic hesitant fuzzy Hamming distance and Euclidean distance are directly and parametrically established by incorporating hesitation degrees; accordingly, the improved distance measures exhibit a \(2\times 2\) $2\times 2$ system on (non-parameter, parameter) and (Hamming, Euclidean), and their distance property, measure size, parameter monotonicity, and promotion degeneration are investigated and acquired. Furthermore, a modified score function is proposed for MEREC to determine attribute weights, and thus a corresponding decision method with TODIM (i.e., MEREC-TODIM) is established for PHFSs applications on evaluation sorting and optimization selection. Finally, MEREC-TODIM is validated through parameter analyses and decision comparisons, and it is effectively applied to two practical examples: Carbon Capture Utilization Storage and PhD Admission Interviews.