Power, principal, and isotone $(\odot ,\vee )$-higher derivations on MV-algebras

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