Fantastic and associative filters in pseudo quasi-ordered residuated systems

An interesting generalization of hoop-algebras and commutative residuated lattices is the concept quasi-ordered systems (shortly QRS) introduced in 2018 by Bonzio Chajda. Quasi-ordered system an integral monoid with two internal binary operations interconnected a residuation connection. This specificity reason for complexity this algebraic structure existence significant number substructures it, such as various types filters. The notion pseudo was developed 2022 author, omitting commutativity requirement QRSs, discussing, additionally, filters it. Concept QRSs QRSs. In report, continuation previous research, addition to introduction concepts fantastic associative system, their mutual connection between them discussed, some examples are presented.