Power, principal, and isotone (☉,∨)-higher derivations on MV-algebras

This paper studies three types of (☉, ∨)-higher derivations on MV-algebras: power, principal, and isotone (☉, ∨)-higher derivations. We show that every principal (☉, ∨)-higher derivation is both power and isotone. However, counterexamples demonstrate that no pairwise implications hold beyond the established one. Furthermore, explicit constructions of power (☉, ∨)-higher derivations are provided. Additionally, we characterize isotone (☉, ∨)-higher derivations and show that the fixed point set of any principal (☉, ∨)-higher derivation forms a lattice ideal.