With the outspread expansion of cloud computing, identifying an appropriate cloud service provider (CSP) needs careful scrutinization and a rational ranking method. Multi-criteria decision-making (MCDM) approaches are considered a hassle-free process that allows selecting the appropriate cloud computing solution based on essential QoS attributes suitable for the enterprise. However, the existing MCDM models are evaluated based on domain-specific qualitative and quantitative QoS values, which have been suffered from uncertainty and hesitancy. For this, linguistic judgments are considered the preferred format for the evaluation process by the decision makers while dealing with vagueness, uncertainty, subjectivity, and randomness. It has been found from the literature that the upheavals of trust due to divergent concerns create restrictions for choosing CSP based on user preferences and functional requirements. Besides, several security challenges have already engulfed the entire world nowadays. Thus, the selection of CSP by keeping the trust factor high and minimizing the security issues is highly in need. In this paper, the cloud model is chosen to consider the randomness and fuzziness of human recognition and convert the linguistic expressions to the crisp weighted matrix. The final ranking of the trusted CSP is selected by the combined compromised solution (CoCoSo) method. Integrating the CoCoSo method with the cloud model brings novelty while selecting the best-preferred solution by the decision makers. The proposed Cloud-CoCoSo model is described with an illustrative case study. It exhibits higher accuracy than the existing models. Further statistical and security analyses have proven the stability and reliability of this approach.