Cloud computing is growing tremendously for its on-demand services, a massive pool of distributed resources, rapid provisioning of resources, and many more. It empowers many organizations/customers to build on-demand applications without investing large capital in creating hardware infrastructure. These organizations encounter numerous challenges towards obtaining full-pledged services from the cloud service providers (CSPs). One such challenge is identifying and deciding upon a suitable CSP that can fulfill the quality of service (QoS) requirements of these organizations. Moreover, the services offered by the CSPs are interrelated and beneficial, and non-beneficial. As a result, it makes it difficult for organizations to suitably evaluate the services rendered by the CSPs. Therefore, multi-attribute decision-making (MADM) algorithms are applied in the literature to overcome the above challenge of uncertainty. In this paper, we survey applications of such algorithms from the perspective of cloud computing. The survey covers both traditional and recent algorithms with their objectives, processes, pros, cons, and implementations. We also present the upcoming challenges and open issues, followed by the performance metrics and tools for their possible implementations. Finally, we conclude by summarizing the survey with some notable remarks.