On derivations of linguistic truth-valued lattice implication algebras

Algebraic characters of linguistic truth-valued lattice implication algebras (L-LIAs) are focused in this paper. Concretely, the concept of derivation coming from analytic theory is introduced in L-LIAs, and then some properties of derivations are given in L-LIAs. Subsequently, some special derivations (such as isotone deri-vation, embedding derivation, isomorphism derivation and regular derivation) are discussed in L-LIAs along with the relations among them. The relations between derivations and lattice implication homomorphisms are also investigated in L-LIAs. At the end, the derivations of some algebraic substructures are described in L-LIAs.

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