Truth values on generalizations of some commutative fuzzy structures

Hájek introduced the logic enriching the logic by a unary connective vt which is a formalization of Zadeh's fuzzy truth value “very true”. -algebras, i.e. -algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of . Residuated lattice ordered monoids (Rℓ-monoids) are common generalizations of -algebras and Heyting algebras. In the paper, we study algebraic properties of Rℓvt-algebras (and consequently of -algebras) and of those that are enriched by derived superdiagonal operators which in the case of MV-algebras are the duals to vt-operators.