We develop an approach allowing to measure the “quality” of rough approximation of fuzzy sets. It is based on what we call “an approximative quadruple” Q =
(L , M, φ, ψ) where L and M are complete lattice commu-tative monoids and φ : L → M, ψ : M → L are mappings satisfying certain conditions. By realization of this scheme, we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with an M-preoder R : X × X → M. In case R is symmetric, these mea-sures coincide. Basic properties of such measures are studied. Besides, we present an interpretation of measures of rough
approximation in terms of L M-fuzzy topologies.

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