Semi-ring Of Rough Sets

Rough Sets as a deal with imprecise, uncertain and incomplete data of the new mathematical theory, were first considered by the Polish mathematician Z. Pawlak in 1982 raised. Nowadays, connected Rough structure with Algebra structure,Topology structure and Order structure, many new prosperous mathematics branches have appeared. In this paper, connected Rough structure with the semirings of Algebra structure, using the concepts of lower(upper)-approximation, we discussed the rough sets in semiring.The dissertation consists of three chapters. In chapter one, the background, the present state of rough sets theory and some fundamental knowledge about semirings are simply introduced. In chapter two, we introduced the concepts of rough left ideal(right ideal, ideal, bi-ideal, quasi-ideal) in semirings, and then have the clusions of that the left ideal(right ideal, ideal, bi-ideal, quasi-ideal) is the rough left ideal(right ideal, ideal, bi-ideal, quasi-ideal) in semirings. Further, we discussed the closeness of rough ideals under the given operations such as products and intersection ect. in semirings. And then, we discussed the invari-ance of rough ideals under the homomorphism in semirings. In chapter three, we extended the properties of commutative rings on rough fuzzy ideals to semirings,and then we have some properties of t-level fuzzy subsets and t-strong level fuzzy subsets in semirings. At last, we discussed the lower(upper)-approximation of fuzzy congruence in semirings.