On algebraic and topological aspects of ILF-automata

This work is toward the study of theory of IF-automata based on residuated lattices ([Formula: see text]-automaton) and to use [Formula: see text]-topological concepts for study of algebraic concepts therein. We introduce the notion of [Formula: see text]-subsystems and strong [Formula: see text]-subsystems of an [Formula: see text]-automaton and show that these are precisely the [Formula: see text]-closed sets with respect to the [Formula: see text]-topologies introduced on state-set of an [Formula: see text]-automaton. Finally, we study the characterization of separated [Formula: see text]-subsystem for an [Formula: see text]-automaton.