For many businesses, cloud computing is essential to their development. Any business that moves its work to the cloud faces the major challenge of choosing the best cloud service provider among the variety of options available, each with unique advantages and benefits. In the case where values are absent from the evaluation of options, the novel framework presented in this study can be used to choose the best provider. The framework is separated into two sections, with the first section focusing on the Modified Generative Adversarial Network (M-GAN) for data imputation of missing data. With the modifications, GAN now has an accuracy of almost 0.91. The second step is the multi-criteria decision-making neutrosophic algorithm for selecting the most suitable provider according to different eight criteria (Availability, Throughput, Successibility, Reliability, Latency, Response time, Response Time of Customer Services, and Cost). According to the experiments done in the paper, the Novel framework has achieved success in choosing suitable providers. It was found that the proposed model obtained accuracy of 91% in 0.05 computation time for 1000 providers.