In order to solve the problem that it is difficult to quantitatively evaluate the interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and deal with the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory, and a linguistic term set is then established to characterize the interactivity between attributes. Secondly, under the linguistic term set, according to the above definition, the experts employ the linguistic expressions generated by the context-free grammar to evaluate the interactivity between attributes, and the opinions of all experts are then aggregated by using the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. Finally, a 2-order additive fuzzy measure identification method based on HFLID is further proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is presented. Taking the credit assessment of the big data listed companies in China as an application example, the feasibility and effectiveness of the proposed method is verified by the analysis results of application example.