Approach to Multi-Attribute Decision-making Based on VIKOR under Q-Rung Orthopair Probabilistic Hesitant Fuzzy Environment

Abstract The q-rung probabilistic hesitant fuzzy sets (q-ROPHFS) can accurately capture the initial information provided by decision makers (DMs), thereby improving the reliability and accuracy of the decision method. A new multi-attribute decision-making (MADM) method combining distance measures of q-rung probabilistic hesitant fuzzy elements (q-ROPHFEs) with the VIKOR is proposed in this paper. Firstly, a distance measurement method under the q-rung orthopair probabilistic hesitant fuzzy environment (q-ROPHFEN) is brought forward. Secondly, a maximum deviation function of q-rung probabilistic hesitant fuzzy elements is presented to determine the weights of attributes when the attribute weights are unknown. Lastly, the VIKOR is extended to solve the probabilistic hesitant fuzzy MADM problem. A numerical example is presented to demonstrate the validity of the above method.