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Web mining is used to search the right information from the Web to meet user information needs. Acquiring correct user profiles is difficult, since users may be unsure of their interests and may not wish to invest a great deal of effort in creating such a profile. Our aim is to present a foundation for representations of user profiles on ontology for designing efficient Web mining models. We assume the user concept can be constructed from some primary ones; hence, we use "part-of" relation to describe the relationships between classes. We also present set-valued relevance functions on such ontology to unravel the relationships between facts and the existing classes. A numerical interpretation is also presented for the set-valued relation functions.