Cubic finite state machine and cubic transformation semigroups

Abstract

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