Abstract

In this article, the notion of a new kind of derivation is introduced for a lattice L called symmetric bi(T, F) derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi(T, F) derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-(T, F)-derivation.