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One of the most important elements in a lattice are the irreducible elements. For example, when the lattice is finite, which is usual in the computational case, it forms a base from which the complete lattice is obtained.These elements are also important in Formal Concept Analysis, since they are the basic information of a relational system.In the general fuzzy framework of multi-adjoint concept lattices, this paper presents a characterization of the irreducible elements and so, a mechanism to detect the base information given in a general relational system. This result is applied to reduce the size of the concept lattices without losing and modifying important information.