State operators on generalizations of fuzzy structures

We enlarge the language of R ℓ - monoids , which are a non-commutative generalizations of both MV algebras and BL algebras, by adding a unary operation that describes algebraic properties of a state (= an analog of probability measures). The resulting algebras are called state R ℓ - monoids and state-morphism R ℓ - monoids . We present basic properties of such algebras. We describe subdirectly irreducible algebras, some generators of the varieties of state-morphism R ℓ - monoids , and an interplay between states and state operators.