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The dynamic resource requirement of applications has forced a large number of business organizations to join the cloud market and provide cloud services. It has posed a challenge for cloud users to select the best service providers and to minimize losses occurring due to its improper selection. This paper aims to propose a robust rank reversal technique for order of preference by similarity to ideal solution (TOPSIS) method based on Gaussian distribution and used to develop a cloud service selection framework. The proposed framework ranks cloud services based on the quality of services provided by cloud service providers and cloud user's priority. A case study is performed on a real dataset obtained from CloudHarmony to show the effectiveness and correctness of the proposed framework. The results obtained demonstrate that the proposed framework ranks cloud services similar to TOPSIS-based frameworks. A sensitivity analysis has also been performed to check its robustness in six different cases causing rank reversal and found that the proposed framework is robust to handle rank reversal phenomenon in all the scenarios in comparison with other studies available in the literature. [ABSTRACT FROM AUTHOR]