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.

Keywords:

(Monadic) MTL-algebras , Monadic filter