  We redefine the quantum-MV algebras starting from involutive BE algebras and
we introduce and study the notion of quantum-Wajsberg algebras. We define the
commutative quantum-Wajsberg algebras and we give a characterization of these
structures. We also prove that any Wajsberg algebra is a quantum-Wajsberg
algebra, and give conditions for quantum-Wajsberg algebras to be Wajsberg
algebras. Furthermore, we prove that Wajsberg algebras are both
quantum-Wajsberg algebras and quantum-B algebras. Finally, we provide certain
conditions for quantum-MV algebras to be MV algebras.

Quantum Algebra