Cubic finite state machine and cubic transformation semigroups

This paper provides a new generalization of fuzzy finite state machines,\nfuzzy transformation semigroups and their relationship. Consider a cubic\nstructure, we introduce cubic finite state machines, cubic transformation\nsemigroups, cubic successor, cubic exchange properties cubic subsystems,\ncubic submachines, cubic q-twins, cubic retrievable and study fundamental\nproperties of them. We provide relationship between cubic $q$-twins and a\ncubic $q$-related. We provide a characterization of a cubic retrievable. We\ndefine cfsm homomorphism and investigated related properties. We show that\nthe composition of strong cfsm homomorphism is also strong. We also define\ncubic transformation semigroup and it related properties. We define cts\nhomomorphism and its properties.