When classical mathematics is applied to green environmental behavior decision making, it is often supposed that information sources with single attribute value, attribute coalition, ordered position and ordered position coalition are independent which is too strong to match decision behaviors in the real world. For real decision making problems, there is always some degree of inter-dependent characteristics between attributes. Usually, there is interaction among preference of decision makers. The Choquet integral only reflects the interaction between two adjacent coalitions. Furthermore, the Choquet integral can either give the importance of elements or that of ordered positions, but it cannot both consider these two aspects. This paper studies the problem for choosing corporate green behavior and proposes a multi attribute decision-making method in which attribute assessments and attribute weight is given in the forms of interval-valued dual hesitant fuzzy assessments. Firstly, the induced generalized interval-valued dual hesitant fuzzy Shapley hybrid weighted averaging (IG-IVDHFSHWAO) operator is proposed and the hybrid multiple attribute decision-making problem is studied. The operator focus on the importance of interval-valued dual hesitant fuzzy elements and their ordered positions, Furthermore, models for the optimal fuzzy measures are established with partial weight of attribute and ordered position, respectively. A method to interval-valued dual hesitant fuzzy information sources multi-attribute decision making under uncertain interval-valued dual hesitant fuzzy information is studied. Secondly, an new non-additive fuzzy measure multi-objective programming (IFMOP) model is proposed with the fuzzy similarity measure. Finally, a practical completive example is provided to illustrate the developed approach. The results of the study show that considering the interdependence between information sources with attributes and ordered positions will make the green corporate environmental behavior choosing decision-making more objective and scientific, as well as expanded the scope of the Shapley independence characteristics on dual hesitant fuzzy information sources.