Cloud service provider selection, an important Multi-Criteria Decision Making (MCDM) problem involves intrinsic relations among the multiple alternatives, attributes and decision experts for the selection of trustworthy Cloud Service Providers (CSPs). Due to uncertain and incomplete nature of the cloud service provider evaluation data, i.e., Quality of Service (QoS) and user feedbacks, the identification of suitable CSPs with accurate service ranking remains an open research challenge. To address the above-mentioned challenge, this work presents an Improved Interval-Valued Intuitionistic Fuzzy Sets-Weighted Aggregate Sum and Product Assessment (IIVIFS-WASPAS) based cloud service provider selection approach for the identification of Trustworthy CSPs (TCSPs). The proposed CSP selection approach employs integrated objective and subjective weight assessment method and IVIFS-WASPAS method to determine the importance of QoS attributes and to rank the TCSPs respectively. Further, a novel preference-attitudinal score and accuracy function of IIVIFS have been designed based on the decision maker’s attitude to rank the TCSPs. Case studies using Cloud Armor, a real-world trust feedback dataset demonstrates the accuracy, effectiveness, and feasibility of IIVIFS-WASPAS approach for CSP selection problem in terms of sensitivity analysis and Rank Reversal Phenomenon (RRP).