Due to the complexity of infrastructure megaprojects, using joint venture contractors (JVCs) is an effective method to deliver projects. However, this process is constrained by several factors, including the quality of competing JVCs and knowledge level of decision-makers (DMs). However, existing decision-making methods for megaprojects and JVC selection lack comprehensive JVC evaluation criteria and cannot handle decision-making scenarios using incomplete data. To address these issues, in this study, we propose a novel model based on a hesitant fuzzy soft set and a linear programming techniques for multidimensional analysis of preferences called LINMAP, which can process incomplete decision data and improve decision accuracy. Moreover, a set of criteria was constructed from four dimensions (economy, society, environment, and cooperation), which upholds the sustainable development and internal cooperation of the built environment. Finally, by applying the approach to a complex infrastructure megaproject and conducting a sensitivity analysis, the feasibility and effectiveness of the proposed model were verified. Research shows that DMs in different specialized areas choose different criterion subsets, which leads to different decision-making results. For one, allowing DMs to choose a subset of the criteria can improve the accuracy of a decision and reduce the accompanying risks; further, a large gap exists between partial and global evaluations, so partial and global consistence must be included in the context of multicriteria decision-making; finally, cooperation is the premise of competition, i.e., good cooperation has a positive effect on competition, so the sustainable development of a JVC needs to consider not only economic, environmental, and social factors but also cooperation. This study contributes to the knowledge domain of multicriteria decision-making, extends the knowledge domain in terms of clarifying complicated evaluation scenarios in infrastructure megaprojects, and renders practical managerial implications for future complex evaluation processes in infrastructure megaprojects.