Fuzzy filters and fuzzy prime filters of bounded Rℓ-monoids and pseudo BL-algebras

Abstract

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. The sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics. Bounded residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of pseudo BL-algebras (and consequently of pseudo MV-algebras) and Heyting algebras, i.e. algebras behind fuzzy and intuitionistic reasoning. In the paper, we introduce and investigate fuzzy filters of bounded Rℓ-monoids and fuzzy prime filters of pseudo BL-algebras.