| To enlarge the usage scope of classical rough sets theory, especially in the intuitionistic fuzzy environment. This paper proposed some new extended models of rough sets by combining intuitionistic fuzzy sets, rough sets and soft sets. Besides, the definition of upper and lower ap-proximations of the new model is given and the properties of the upper and lower approximation and the relationships between these models are discussed.? In this paper, a new model called soft rough intuitionistic fuzzy sets is given by using soft sets to granulate the universe of discourse, which can be seen as an extension of rough intuitionistic fuzzy sets. On the basis of it, a new hybrid model called soft intuitionistic fuzzy rough sets is proposed by using intuitionistic fuzzy soft sets to granulate the universe of discourse. which can be seen as an extension of soft rough intuitionistic fuzzy sets.? Based on a pair of border implications (I. J), a new model of (I. J)-soft intuitionistic fuzzy rough sets is proposed by combining soft intuitionistic fuzzy rough sets. On the basis of it, the relationship between (I, J)-soft intuitionistic fuzzy rough sets and intuitionistic fuzzy rough sets is also discussed.? Based on the soft intuitionistic fuzzy approximation space, a new model of multi-granulation intuitionistic fuzzy soft rough sets is proposed by combining soft intuitionistic fuzzy rough sets. Based on a pair of border implications (I. J), the model of (I. J)-optimistic multi-granulation intuitionistic fuzzy soft rough sets is proposed by combining the idea of multi-granulation and the related properties are investigated. |
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