An ORESTE approach for multi-criteria decision-making with probabilistic hesitant fuzzy information

As an important extension of fuzzy number, the probabilistic hesitant fuzzy element (PHFE) shows the flexibility of decision makers in expressing hesitant information in multi-criteria decision-making (MCDM) processes. Accordingly, numerous research findings have been obtained since PHFE introduction. However, a few important issues in PHFE utilization remain to be addressed. This study introduces the French organization Rangement Et Synthese De Ronnees Relationnelles' (ORESTE) approach for MCDM with probabilistic hesitant fuzzy information. First, the limitations of normalized PHFE (NPHFE), Euclidean distance, and several operations in previous studies are discussed. Subsequently, an algorithm is designed to derive the new NPHFE. A new Euclidean distance and several operations are developed on the basis of the proposed NPHFE. Second, the ORESTE approach is extended to probabilistic hesitant fuzzy environments. Lastly, the problem of selecting best research topic is presented to demonstrate that the proposed approach is effective. A comparative study with other approaches is conducted with identical illustrative example.