The development of information and communications technology has led organizations to use various solutions to meet their communication needs. One of the best practices for this purpose is the use of cloud computing. Cloud computing allows users to access IT-based services without having to specialize in or control technology infrastructure. At the moment, there are several software applications for implementation of cloud computing in organizations, which make it difficult to select the appropriate tool for the organization. This paper aims to help select the appropriate software for cloud computing system implementation at the Faculty of New Sciences and Technologies, Tehran University. For this purpose, at first, the appropriate criteria are extracted from the related literatures and then finalized using expert opinions. Then, by using an interval-valued intuitionistic fuzzy CODAS multiattribute decision-making method, the criteria are weighted and the alternatives are prioritized. The results indicate that the open stack cloud computing system can be selected as the best alternative. Choosing this alternative can be due to its remarkable distinction in criteria such as performance, system reliability and security, system stability, usability, serviceability, and being open source. According to the experts of this project, the most important criteria for decision making are software availability and system reliability and security.