Abstract
In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.