The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded Rl-monoids.
Bounded residuated lattice ordered monoids (Rl-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV-algebras (or, equivalently, GMV-algebras) and pseudo BL-algebras (and so, particularly, MV-algebras and BL-algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on MV-algebras were studied by Harlenderová and Rachůnek (2006) and on bounded commutative Rl-monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded Rl-monoids which need not be commutative and investigate their properties also for further derived algebras.