($\odot$, $\vee$)-derivations on MV-algebras

Let $A$ be an MV-algebra. An $(\odot,\vee)$-derivation on $A$ is a map $d: A\to A$ 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.