We propose a web service registry, a broker that mediates between service providers and service consumers, considering that a service consumer is a developer of web service-based composite applications. This registry enables providers of publishing their well-described documented services, and providing their estimated QoS information related to these services. It adapts two classifying techniques: Formal Concept Analysis (FCA) and Relational Concept Analysis (RCA). The published services are organized into domains of functionality and in each domain similar services are classified in order to reveal replaceable services. We build our classification using FCA, which is a method of data analysis that takes as input a set of objects and a set of attributes with the relation between them indicating which objects have which attributes. After analyzing the input data, it clusters the objects into concepts depending on their attributes, and reveals the relationships between these concepts, thus, the relationships between the objects. The concepts can then be ordered in a lattice structure for a better browsing and navigation of objects and relationships among them. We adapt this method for classifying web services by considering that the set of objects is a set of web services, and the set of attributes is the set of the offered operations. The resulting classification is represented as a concept lattice for web services, from which we can easily select a needed service by browsing its offered operations, and we can also find the possible substitutes of a selected service. Using this method, services are also classified according to their QoS attributes specified by the providers. This enables services consumer of finding an aimed service depending on its functional and non-functional aspects, as well as finding its possible substitutes. A service consumer may either query the registry for services offering a specific operation, or he can design an abstract business process that describes his aimed composite application, in which he specify the set of needed tasks ordered in a workflow. The registry will analyze the specified abstract process and finds the set of web services that can fulfill each task, by querying the corresponding service lattice. After discovering the sets of services that can fulfill the tasks in order to satisfy the functionality required by the abstract process, another classification is built that reveals the composable services according to each pair of consecutive tasks. This second classification is based on an extension of FCA called RCA.