On subsystems of a hybrid finite state machine

Humanity’s efforts are manifested in the creation of novel solutions to complex problems in diverse fields. Traditional mathematical methods fail to solve real-world problems due to their complexity. Researchers have come up with new mathematical theories like fuzzy set theory and rough set theory to help them figure out how to model the uncertainty in these fields. Soft set theory is a novel approach to real-world problem solving that does not require the membership function to be specified. This aids in the resolution of a wide range of issues, and significant progress has recently been made. After Jun et al. came up with a hybrid system that combined fuzzy and soft set concepts, many people came up with hybrid ideas in different algebraic structures. In this paper, we introduce the concepts of subsystem and strong subsystem of a hybrid finite state machine (HFSM) and investigate a portion of their significant properties. We also provide an example that shows that every subsystem does not need to be a strong subsystem. Additionally, we study the cyclic subsystem of HFSMs and also obtain their equivalent results and examples. Finally, we define the notions of homomorphism of subsystems and strong subsystems of HFSMs.