The evolution of Service-Oriented Computing (SOC) provides more efficient software development methods for building and engineering new value-added service-based applications. SOC is a computing paradigm that relies on Web services as fundamental elements. Research and technical advancements in Web services composition have been considered as an effective opportunity to develop new service-based applications satisfying complex requirements rapidly and efficiently. In this paper, we present a novel approach enhancing the composition of semantic Web services. The novelty of our approach, as compared to others reported in the literature, rests on: i) mapping user's/organization's requirements with Business Process Modeling Notation (BPMN) and semantic descriptions using ontologies, ii) considering functional requirements and also different types of non-functional requirements, such as quality of service (QoS), quality of experience (QoE), and quality of business (QoBiz), iii) using Formal Concept Analysis (FCA) technique to select the optimal set of Web services, iv) considering composability levels between sequential Web services using Relational Concept Analysis (RCA) technique to decrease the required adaptation efforts, and finally, v) validating the obtained service-based applications by performing an analytical technique, which is the monitoring. The approach experimented on an extended version of the OWLS-TC dataset, which includes more than 10830 Web services descriptions from various domains. The obtained results demonstrate that our approach allows to successfully and effectively compose Web services satisfying different types of user's functional and non-functional requirements.