Cloud computing technology (CCT) provides virtual services accessible to its users from anywhere based on subscriptions with attractive costs wherever they are. It also brings many different benefits to businesses as well as the public by saving them time and resources that would be needed for establishing and operating their own Information Technology infrastructure. For this reason, the objectives of this study are to identify important decision criteria and sub criteria that are relevant to the CCT selection problem; to provide an effective framework to evaluate and select the most appropriate CCT and to apply proposed approach through an empirical study. Technology selection in general is a complicated multi-criteria problem that concerns both quantitative and qualitative parameters, which are usually conflicting and uncertain. Interval Valued Intuitionistic Fuzzy (IVIF) set is a powerful method to cope with uncertainty by taking both degree of membership and non-membership function in an interval. Therefore, a multi-criteria analysis and solution methodology is presented, which incorporates decision makers' insufficient knowledge and other pressures involved in the evaluation with the help of an extension of MULTIMOORA (Multi-objective Optimization by Ratio Analysis plus the Full Multiplicative Form) technique in order to rank alternatives for handling imprecise data in selecting the most suitable CCT. To demonstrate the usability of the proposed technique, an illustrative study is also given.