Several Properties Of Fuzzy Semirings On Star Operation

In this paper, we define star operation for fuzzy sets, and study several properties of fuzzy semirings based on it. Firstly, some important and elementary concepts that are frequently used in the remaining chapters are provided. Secondly, star operation for fuzzy sets is defined, fixed point equation is proved hold when fuzzy sets satisfies the fixed point inequation and fixed point induction rule, and several properties of star operation are studied. Moreover, the expression of least fixed (prefixed) point for fuzzy linear function is performed on star operation, and the equivalence between the expression of least fixed (prefixed) point on star operation and the fixed point induction rule for fuzzy sets is proved hold. Finally, fuzzy formal power series and star operation on it are induced by formal power series of semirings, and fuzzy formal power series have the nature of their properties when fixed point induction rule and least the expression of fixed point rule held in fuzzy semiring are proved.