In this paper we present an extension of the Galois connection to deal with many-valued formal contexts. We define a many-valued Galois connection with respect to similarity between attribute values in a many-valued context. Then, we define many-valued formal concepts and many-valued concept lattices. Depending on a similarity threshold, many-valued concept lattices may have different levels of precision. This feature makes them very useful for multilevel conceptual clustering. Many-valued concept lattices are also used in a new lattice-based information retrieval approach for efficiently answering complex queries.