| Firstly,This paper considers determinate knowledge systems (U , F , LL , HH ) and (U ,σ( J ), LL , HH). It discusses that the condition of the operation of set-algebra that is the closure of (?), (?),～weakens to olny request the closure of (?,)～or the closure of (?),～. So we obtain their some properties,and generalize the corresponding results.Secondly,this paper considers three kinds of fuzzy concept information granularity and discusses the methods of transforming a pair with any object set and attribute set into a fuzzy concept of concept knowledge systems. We obtain certain knowledges between the object and attribute.Thirdly,this paper combines interval-valued intuitionistic fuzzy sets and rough sets. It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic rough fuzzy sets model under the equivalence relation in crisp sets. That extends the classical rough set defined by Pawlak. Then the generalized concept of cut sets of interval-valued intuitionistic fuzzy sets was introduced. Some properties of cut sets of interval-valued intuitionistic fuzzy sets were discussed. And,decomposition theorem and representation theorem of interval-valued intuitionistic fuzzy sets were given.Finally,it introduces the application of interval-valued intuitionistic fuzzy soft sets in decision making problem. The interval-valued intuitionistic fuzzy soft rough sets , interval-valued intuitionistic fuzzy soft cut sets, interval-valued intuitionistic fuzzy soft decomposition theorem and interval-valued intuitionistic fuzzy soft representation theorem are established. Their basic properties are also presented and discussed.
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