| Rough set theory is not only a new mathematical tool dealing with vagueness and uncertainty but also a new and effective soft computing method.It was been widely used in the area of machine learning,knowledge discovery,decision anaysis,artificial intelligence,date mining,pattern recognition,ect.At some time,some articles that have been studied about the theory combined pure mathematics with rough sets have been emerged,and some new mathematical notions,such as rough ideal insemigroups,rough invariant subgroups,rough groupsand rough subgroups,homomorphism and isomorphism of rough groups,are introduced.Certainly,with integration of rough structure and algebra structure,topology structure,order structure and the other structure,some new vital mathematical branches will be emerged. In addition,extention of the premitive model is a main current direction of study,The chief way are by the way of structural and algebral.In this paper,the main work is to extended the premitive model of rough sets;Accorting to the Rough structure and algebra structure,the main work is to study the application of rough set theory on algebra system-group,so that rough algebra system is better perfectly.The general process as follows:1. Upgraded their universes to their power sets, the concept of rough power sets will be raised firstly and point out several related properties; The premitive model of rough sets is extended by the way of structural,The model of rough set on the double universe is advanced and point out several related properties; discussed the algebraic property of assistant sets of single-direction S-rough sets in approximate space.2. Discussed the algebra system of the rough set, introduces such concepts as rough-fuzzy subgroup, gives several relations properties; upgraded their universes to their power sets, the concept of rough hypergroup will be raised firstly and point out several related properties;discussed the application of rough sets theory on decision analysis, Using measures of...
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