Information technology is building communications networks for a company, safeguarding data and information, and creating and administering databases. Currently, cloud computing provides a single set of physical resources for providing multiple information technology (IT) services to a large user base with varying needs. With the advent of multi-cloud computing, abundant web services are published by several providers to their worldwide users. Web service composition technology attracted a lot of attention for the sake of reduction in software development costs. In a multi-cloud environment (MCE), each atomic web service published by any cloud provider with the same functionality has a different price and quality of service (QoS). Service discovery and composition are the key challenges for web services development. The challenges in the composition of services distributed in multi-cloud environments include increased cost and a reduction in its speed due to the increasing number of services, providers, and clouds. Consequently, to overcome these challenges, the QoS-aware multi-cloud web service composition is presented in this work. The research work initially proposed a Deep Neural Network (DNN) aim of the study is to recommend the web service composition. The proposed method recommends the matched services to the user based on the user's need. Subsequently, a Hybrid Firefly and Bee Colony Optimization Algorithm is introduced for the Multi-cloud service composition problem of NP-Hard in a multi-cloud environment. The proposed optimization algorithm reduces the number of cloud providers to provide the best services. Additionally, the security of multi-cloud web service composition is important, to provide this security, a Fuzzy Generalized Rough Set Theory is presented in this paper. Accordingly, this fuzzy rough set theory eliminates insecure services. Subsequently, the proposed work is implemented using Python software. The performance metrics are throughput, response time, availability, feasibility, efficiency, etc. The proposed method is compared with the existing BOTV-PSO, MLTS-MCSC, IWD, and GNN-QSC. Subsequently, compared to these existing methods, the proposed method is 2% more than the existing methods for execution time, for response time, the proposed method is approximately 3% higher than the existing methods. The proposed method is 5% higher than the existing methods for availability and 4% higher for throughput. The proposed work performs the best service composition to the user and in future determines the minimum and maximum allowable used clouds to minimize the communication costs in a multi-cloud environment respectively.