We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras (multi-valued algebras) and we show that the class of all effects of any Hilbert space (positive linear operators between 0 and 1) gives rise to an example of such a structure. Effects are the main ingredients of the so-called unsharp (or operational) approach to quantum mechanics and replace projectors as possible candidates for the notion of "experimental proposition". We present some algebraic and structural properties of QMV algebras, claiming that these structures represent non-idempotent extensions of orthomodular lattices.

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