Cloud Computing has gained substantial popularity due to its ability to offer diverse and dependable computing services suited to clients demands. Given the rapid expansion of this technology, an increasing number of IT service providers are competing to deliver cloud services that are both of excellent quality and cost-efficient, in order to best meet the requirements of their clients. With the extensive range of options available, selecting the best Cloud Service Provider (CSP) has become a challenging dilemma for the majority of cloud clients. When evaluating services offered by many CSPs, it is important to consider multiple attributes. Efficiently addressing the selection of the best CSP involves tackling a challenging Multi-Attribute Decision Making (MADM) problem. Several MADM techniques have been proposed in academic literature for evaluating CSPs. However, the persisting problems of inconsistency, uncertainty, and rank reversal remain unresolved. In this paper the authors present a hybrid MADM framework to rank eight CSPs using nine Quality of Service (QoS) attributes. In order to achieve this objective, Fermatean fuzzy sets-full consistency method (FFS-FUCOM) is combined with Grey-Relational-Analysis and the Technique-for-Order-Preference-by-Similarity-to-Ideal-Solution (Grey-TOPSIS) technique. The framework successfully resolved the aforementioned problems. Sensitivity analysis is conducted to assess the stability and robustness of the results produced by the proposed framework. The sensitivity analysis results indicate that the proposed framework offers an accurate and robust solution. A systematic ranking test is undertaken to ensure that the results are ranked in a systematic manner. Additionally, a comparative analysis is carried out with the most relevant study.