Co-derivative and derivative operators on commutative bounded integral residuated lattices

In this paper we introduce and investigate multiplicative co-derivative operators and additive derivative operators on commutative bounded integral residuated lattices. Moreover, we represent con-nections between multiplicative co-derivative operators and additive derivative operators on commutative bounded integral residuated lattices. Also, we indicate that multiplicative co-derivative operators are generalizations of multiplicative interior operators on this lattices. Then we describe connections between multiplicative co-derivative operators (additive derivative operators) on commutative bounded integral residuated lattice with Glivenko property and on the residuated lattices of their reguler elements. Finally, we study some properties of the commutative bounded integral residuated lattices with multiplicative co-derivative operator.