Areas Of Coarse Soft Sets And Rough Sets

There are four parts in this paper. In part one, we give the definition ofrough soft sets(RSS) first. Next, we define the rough soft subset of a RSS, complementrough soft set of a RSS, intersection of two RSSs and union of two RSSs, etc. Againwe study the two RSS's operation and property of the RSS. At last, we give an ap-plication of RSS in a decision making problem. Similarly, we discuss rough fuzzy softsets(RFSS) and rough intuitionistic fuzzy soft sets(RIFSS) respectively in the followingtwo parts. At the last part, we study I-rough-sets as a category. First we build thecategory of I-rough-sets(RS). Then we verify the topos property of RS and find thatRS has all topos properties except one, for it has no subobject classifier(SC). There-fore RS is not a topos. But we find a middle object in RS. By the definition of weaktopos given by professor Xue-hai Yuan, we proofed that the category RS is a weak topos.