Semantic of intuitionistic fuzzy rough logic and its reasoning

The theory of the intuitionistic fuzzy rough set is introduced into the logic reasoning. By the combination of such basic theories as rough sets,intuitionistic fuzzy sets and mathematical logic,the semantic and reasoning methods of intuitionistic fuzzy rough logic are given. Initially,five logic values for the intuitionistic fuzzy proposition logic are given,i.e. intuitionistic fuzzy true,intuitionistic fuzzy false,intuitionistic fuzzy rough true,intuitionistic fuzzy rough false and intuitionistic fuzzy rough incompatible,and on the basis of this,the intuitionistic fuzzy rough logic operations are given; then the semantic of intuitionistic fuzzy rough proposition formulas in approximate space is discussed; finally,the semantic reasoning methods are proposed as for the intuitionistic fuzzy rough propositional formula containing different logical conjunctions.