Classes of filters in generalizations of commutative fuzzy structures

Abstract

summary:Bounded commutative residuated lattice ordered monoids ($R\ell$-monoids) are a common generalization of $\mathit {BL}$-algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative $R\ell$-monoids