Today, organizations are faced with a multitude of projects and investment opportunities, which has made the decision to choose an organizational project due to the complexity of project evaluation and also limited resources face many challenges. Many studies have been performed to present and evaluate the performance of models and algorithms of project portfolio optimization. However, in terms of interactions between projects, many of these studies have been overlooked. This article deals with the issue of electronic project portfolio selection by considering the interactions between projects. For this purpose, a new one-objective linear programming model of integers zero and one, based on gray theory and in conditions of uncertainty, has been developed. In this regard, two multi-criteria utility objective functions have been developed to investigate the conditions for interactions. Finally, the performance of the proposed model is evaluated with a numerical example and the results of its implementation are presented. The results show that the organizational project portfolio selection model has a better performance compared to ignoring these effects by considering the interactions between projects. In fact, the proposed model illustrates the fact that considering the interactions in the project portfolio selection process will create synergies and prevent the selection of projects that are competitive with each other. © 2021 KIIE