Industry 4.0, the new vision of our age has forced companies to transform their processes. In the process of transition to Industry 4.0, one of the most crucial success factors is to select the project portfolio that best fits their objectives. The uncertainty included in the projects, the interproject priority, and various interdependence relations, interactions between project evaluation criteria, decision makers with different perspectives, and preferences make Industry 4.0 project portfolio selection decision considerably complicated. In this study, a two-stage fuzzy approach is proposed to address this complex problem. In the first stage of the approach, the main criteria and subcriteria to be used in evaluating the Industry 4.0 projects have been determined based on the literature review and expert opinions. Following this, a network structure representing outer and inner dependencies has been formed, and the priority weights of the criteria have been obtained by taking into consideration these dependencies. Then, each of the project alternatives has been evaluated under subcriteria, and desirability indexes of project alternatives have been calculated. Fuzzy analytic network process has been applied in this stage. In the second stage, fuzzy multi-objective nonlinear programming has been used to select a project portfolio. In the application of the first stage of the proposed methodology, experts from three firms, which have made significant progress in the Industry 4.0 implementation process, are the decision makers. In the application of the second stage, hypothetically created project alternatives and their dataset have been used.