中文摘要：

讨论模糊有限状态机的一些代数性质，得到模糊有限状态机在同态作用下子系统（强子系统）的前像仍是子系统（强子系统），证明若两个模糊有限状态机之间存在满足一定条件的同态映射时，前一个模糊有限状态机是强连通的（循环的），则后一个模糊有限状态机也是强连通的（循环的），且若这个同态是强满同态，则其中一个模糊有限状态机是完全的当且仅当另一个模糊有限状态机是完全的。对模糊有限状态机的积与原来的模糊有限状态机的完全性、强连通性、循环性、交换性等关系也进行讨论，得到一些结果。

英文摘要：

In this paper, we discuss some algebraic properties of a fuzzy finite state machine, we obtain the preimage of the subsystem （strong subsystem） of a fuzzy finite state machine under homomorphism is also a subsystem （strong subsystem ）, and we prove when the homomorphisms of fuzzy finite state machines satisfy some conditions, the first fuzzy finite state machine is strongly connected （cyclic）, then the second fuzzy finite state machine is also. When this homomorphism is an onto strong homomorphism, then one fuzzy finite state machine is complete if and only if the other is complete. Finally, the relations between the products of fuzzy finite state machines and the fuzzy finite state machine, for example, the completeness, strongly connexity, cyclicity, commutativity and so on are studied.