Subsystems and Fuzzy Relation Equations of Fuzzy Automata Based on Generalized Residuated Lattice

The objective of this paper is to establish the concepts of subsystems, reverse subsystems and double subsystems of a fuzzy automata based on generalized residuated lattices where the fuzzy sets are equipped with generalized residuated lattice in which the commutative property does not hold and characterizes them in terms of fuzzy relation inequalities and equations. Also, the opening and closure systems in the lattices of fuzzy subsets of Q can be discussed for these six subsystems.