Let A be an MV-algebra. An \((\odot ,\vee )\) -derivation on A is a map \(d: A\rightarrow A\) satisfying: \(d(x \odot y) = (d(x) \odot y) \vee (x \odot d(y))\) for all \(x, y \in A\) . This paper initiates the study of \((\odot ,\vee )\) -derivations on MV-algebras. Several families of \((\odot ,\vee )\) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of \((\odot ,\vee )\) -derivations. Furthermore, \((\odot ,\vee )\) -derivations on a finite MV-chain are enumerated and the underlying lattice is described.
