Some types of filters in residuated lattices
In this paper, inspired by some types of \(BL\)-algebra filters (deductive systems) introduced in Haveshki et al. (Soft Comput 10:657664, 2006), Kondo and Dudek (Soft Comput 12:419423, 2008) and Turunen (Arch Math Log 40:467473, 2001), we defined residuated lattice versions of them and study them in connection with Van Gasse et al. (Inf Sci 180(16):30063020, 2010), Lianzhen and Kaitai (Inf Sci 177:57255738, 2007), Zhu and Xu (Inf Sci 180:36143632, 2010). Also we consider some relations between these filters and quotient residuated lattice that are constructed via these filters.
filter residuated lattice deductive system bl-algebra mv-algebra boolean algebra tarski algebra hilbert algebra latticeal filter boolean deductive system implicative deductive system implicative filter positive implicative filter fantastic filter mv-filter easy filter