Cloud computing technology (CCT) can bring considerable advantages to businesses and people by taking over many time-wasting technicalities, such as establishing communications infrastructure, thus adding value. CCT is revolutionizing every industry by allowing all types of organizations to buy a service instead of owning with flexible rates. An objective of this study is to identify a set of relevant decision criteria and their subcriteria needed in the evaluation of the CCT provider selection (PS) problem. Another objective is to provide a powerful integrated framework that can be used for the evaluation and selection of the most appropriate CCT provider and then to apply this proposed approach in a real case study. CCT PS is a complex multi-criteria decision problem that involves a number of qualitative and quantitative parameters that might be conflicting, or even ambiguous. Interval-valued intuitionistic fuzzy (IVIF) set is an effective concept that is used to cope with uncertainty by taking both the degree of membership and non-membership functions in an interval. Therefore, this paper proposes a state-of-the-art novel methodology consisting of IVIF analytic hierarchy process, IVIF complex proportional assessment, IVIF multi-objective optimization by ratio analysis plus the full multiplicative form, IVIF technique for order of preference by similarity to ideal solution and IVIF viekriterijumsko kompromisno rangiranje methods. This combination aims to rank available CCT PS alternatives in the presence of imprecise and vague information.