a novel species on mtl-algebras

In this paper, we investigate monadic mtl-algebeas that can be caught as a extention of algebraic models of the predicate calculi of those logics. firstly, we define monadic mtl-algebras: a variety of mtl algebras equipped with two unary operators.also, the vital properties of this algebra are given. moreover, we introduce and study monadic filters in the monadic mtl-algebras. by this concept, representable monadic mtl-algebras were characterized. in addition, the notion of subdirectly irreducible monadic mtl-algebras have been defined and some basic properties of them have been determined.