Products of cyclic fuzzy finite state machines

A cyclic fuzzy finite state machine is a fuzzy finite state machine which is generated by a state.In this paper, we study products of cyclic fuzzy finite state machine.We prove that two cyclic finite state machines are cyclic when the full direct product(or restricted direct product, or cascade product, or wreath product) of them is cyclic.However, products of two cyclic fuzzy finite state machines are not necessarily cyclic.We introduce the concept of strong cyclic fuzzy finite state machine, and prove that products(including full direct product, restricted direct product, cascade product and wreath product ) of two strong cyclic fuzzy finite state machines are strong cyclic.