Fusions and preference relations based on probabilistic interval-valued hesitant fuzzy information in group decision making

This paper proposes probabilistic interval-valued hesitant fuzzy set (P-IVHFS) by integrating the probability distribution into IVHFS. The concept can make some vital but seemingly repetitive information [such as the same memberships of interval forms given by different decision makers (DMs)], which is an important basis for decision-making rather than being discarded. Moreover, some operations and aggregation operators of probabilistic interval-valued hesitant fuzzy elements (P-IVHFEs) and probabilistic interval-valued hesitant fuzzy preference relation (P-IVHFPR) are put forward, based on which, a decision-making model is proposed. It can keep almost all information given by the DMs so that the results calculated with the model will be much more reliable than those calculated with approaches based on IVHFSs. Finally, a practical case concerning the evaluation of intelligent transportation systems is given to verify the advantages of the proposed decision-making approach based on P-IVHFPRs.