A Novel Choquet Integral-based VIKOR Approach under Q-rung Orthopair Hesitant Fuzzy Environment

Q-rung orthopair hesitant fuzzy set (q-ROHFS) is a potent and effective technique for dealing with more general and complex uncertainty. Multiple attribute decision-making (MADM) under complex uncertainty has been a key research issue. However in the existing MADM approaches, the fuzzy entropies involve much higher hesitancy degree loss and the fuzzy measure of attributes can not be determined objectively. Also these existing MADM methods under complex uncertainty have high data redundancy and low computational efficiency. In order to solve these problems, this paper proposes a novel q-rung orthopair hesitant fuzzy information MADM method based on the Choquet integral. Firstly, we give the axiomatic definition of q-rung orthopair hesitant fuzzy entropy (q-ROHFE) by extending dual hesitant fuzzy information entropy and derive the fuzzy entropy construction theorem and the two related q-ROHFE formulas, which greatly reduces the loss of hesitancy degree resulting from the existing fuzzy entropy. Secondly, combined with λfuzzy measure and proposed q-ROHFE, a constrained nonlinear fuzzy measure optimization model for q-rung orthopair hesitant fuzzy decision making is presented, which addresses the difficulty that existing research cannot determine the fuzzy measure of attributes under fuzzy MADM. Thirdly, an improved Choquet integral-based VIKOR approach based on the fuzzy measure computed by the model is developed. Finally, two real-life cases are shown to fully illustrate the suggested approach. Experiment results demonstrate that the proposed fuzzy entropy has much less hesitancy degree loss and the proposed approach significantly increases computational efficiency while reducing data redundancy. And our method has strong adaptability and scalability.