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Based on the probabilistic interval-valued hesitant fuzzy information aggregation operators, this paper investigates a novel multi-attribute group decision making (MAGDM) model to address the serious loss of information in a hesitant fuzzy information environment. Firstly, the definition of probabilistic interval-valued hesitant fuzzy set will be introduced, and then, using Archimedean norm, some new probabilistic interval-valued hesitant fuzzy operations are defined. Secondly, based on these operations, the generalized probabilistic interval-valued hesitant fuzzy ordered weighted averaging (GPIVHFOWA) operator, and the generalized probabilistic interval-valued hesitant fuzzy ordered weighted geometric (GPIVHFOWG) operator are proposed, and their desirable properties are discussed. We further study their common forms and analyze the relationship among these proposed operators. Finally, a new probabilistic interval-valued hesitant fuzzy MAGDM model is constructed, and the feasibility and effectiveness of the proposed model are verified by using an example of supplier selection.

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Recent frequent “thunderstorm incidents” of P2P lending industry have caused the panic of industry investors. To predict the investment risk of P2P lending, we should scientifically and rationally analyze the key influencing factors of P2P lending investment risk. Existing key influencing factors selection methods mainly involve traditional statistical approaches and artificial intelligence methods. The traditional statistical approaches cannot deal with the high-dimensional nonlinear problems, and it cannot find the exact key influencing factors of the P2P lending investment risk. The artificial intelligence methods cannot recognize and learn the application background, and the selected attributes without active thinking and personal perception may not be the key influencing factors of P2P lending investment risk. To address the above issues, a novel key influencing factors selection approach of P2P lending investment risk is proposed by combining the proposed fireworks coevolution binary glowworm swarm optimization (FCBGSO), multifractal dimension (MFD), probit regression, and artificial prior knowledge. First, multifractal dimension combined with the proposed FCBGSO is used to select the preliminary influencing factors of the investment risk; second, the nonsignificant relevant attributes in the preliminary influencing factors are removed using the probit regression, and we add the influencing factors extracted from the original dataset of P2P lending using the artificial prior knowledge into the retaining influencing factors after removing one by one. A small and reasonable number of influencing factor subsets are achieved. Finally, we evaluate each influencing factors subset using extreme learning machine (ELM), and the subset with the best classification accuracy is efficiently achieved, i.e., it is the key influencing factors of P2P lending investment risk. Experimental results on the real P2P lending dataset from the Renrendai platform demonstrate that the proposed approach performs better than other state-of-the-art methods and that it has validity and effectiveness. It provides a new research idea for the key influencing factors selection of P2P lending investment risk.