On weak covering of products of fuzzy finite machines

In order to clarify the complicated relationship among the products of fuzzy finite machines, the product structure is studied in this paper. By introducing the concept of weak covering, the correlations among the product automata can be contacted availably. Applying algebraic techniques, the more covering relationship has been established in the products of fuzzy finite machines than before. The definition of weak covering is given; the covering relationship between wreath products and cascade products is proven. The weak covering relationship can effectively describe and simplify the product structure of fuzzy finite machines.