Nowadays, governments are cooperating with the private sector under the name of public-private partnership (3P) projects in order to reduce the risks of projects and to achieve the ultimate goal, which is the construction and operation of the project. In order to help decision makers and managers to make decisions in 3P projects, this article examines the financial challenges of the project in uncertain conditions with an intuitive fuzzy approach. The intuitionistic fuzzy multi-criteria weighting and ranking model (IF-MCWR) proposed method based on the intuitionistic fuzzy values to compute the weighting and ranking of the criteria. In process of the proposed IF-MCWR model, criteria's weights are generated to reduce the errors. Also, criteria with optimal weights are obtained based on IF Hamming distance measure by utilizing an extended maximizing deviation approach. Furthermore, judgments of decision makers (DMs) and experts are taken into account for calculating the criteria’ weights. Nevertheless, weights of experts are shown based on proposed new IF technique for order performance by similarity to ideal solution method. Then, based on hamming distance, a new IF index measure is proposed to obtain the relative closeness coefficient for ranking the candidates or alternatives. By doing this, project managers can make decisions with a more confident view. Finally, a case study is presented that examines the issue of urban development and presents the option of constructing a highway project as the most important and highest ranking among the projects that brings the most financial challenge.