With the development of the cloud computing era, the decision-making environment and algorithm models have become increasingly complex, and traditional decision-making methods have been unable to meet the needs of large group decision-making (LGDM) problems. Firstly, in order to solve this problem, the concept of double hierarchy interval hesitant fuzzy language (DHIHFL) is proposed. Compared with the traditional double hierarchy hesitant fuzzy language (DHHFL), it contains all elements from the lower limit to the upper limit and more comprehensively characterizes the hesitation of language information. Secondly, for LGDM problems, a self-confident double hierarchy interval hesitant fuzzy language (SC-DHIHFL) is developed, and the integration of self-confident degree can better enrich the evaluation information and promote the achievement of group consensus. Thirdly, a new two-stage LGDM method is proposed. The first stage is clustering and grouping and reaching consensus within the group, and the second stage is the integration of LGDM information. The two-stage method contains novel methods such as expert clustering algorithm, subjective and objective comprehensive weight, consensus degree, and deviation weight considering minority opinions. Finally, the proposed LGDM consensus method is applied to a practical LGDM problem, and the effectiveness is verified by comparative analysis with existing methods.