| As two powerful knowledge discovery tools, rough set theory, proposed by Pawlak and concept lattice theory, proposed by Wille have been used to study and present the implicit knowledge in data analysis, knowledge hidden in information systems may be unraveled through knowledge reduction. These two theories are gradually becoming a hot field in the research of artificial intelligence. In data explosion era, with the increasing complexity and uncertainty of the data, the objective description of data is an urgent problem to solute. The more objective the description of data is, the better role rough set theory and concept lattice theory will play in data analysis. Intuitionistic fuzzy set theory, proposed by Atanassov is considered as an enrichment and extension of Zadeh's fuzzy sets. On the basis of ortho-pairs of fuzzy sets by employing membership degree and non-membership degree, the description of data is more delicate and objective. Recently, intuitionistic fuzzy set theory has been successfully applied in decision analysis and pattern recognition.In this thesis, we study the representation of knowledge in intuitionistic fuzzy environ-ment. Combining with rough set theory, we study the algebraic structure of intuitionistic fuzzy rough approximation operators. Combining with the theory of concept lattice, we study the constructive method of intuitionistic fuzzy concept lattice and attribute reduction. The main results in this thesis are summarized as follows:1. The algebraic structure and uncertainty measures of (I-T>intuitionistic fuzzy rough sets are studied. The basic granule of (I- T)-intuitionistic fuzzy rough sets is proposed by intuitionistic fuzzy logical operators, some properties of the basic granule under some special intuitionistic fuzzy relations are discussed. We also study the granular structure of (I - T)-intuitionistic fuzzy rough sets. Roughness measure of (I-T)-intuitionistic fuzzy rough sets is defined, some properties of roughness measure are studied.2. The connection of (I - T)-intuitionistic fuzzy rough sets and group structure is studied. (I - T)-intuitionistic fuzzy normal subgroups and the product of intuitionistic fuzzy sets are defined, some properties of T-intuitionistic fuzzy normal subgroups are discussed. T-similarity intuitionistic fuzzy relation on a group is induced by a T-intuitionistic fuzzy normal subgroup, thus (I - T)-intuitionistic fuzzy rough sets on a group are established. The product structures of (I-T)-intuitionistic fuzzy rough sets on a group are studied. Some properties of (I-T)-intuitionistic fuzzy rough approximation operators under a group homomorphism are examined.3. The constructive method and attribute reduction of intuitionistic fuzzy concept lattice are studied. The constructive method of concept in certain level of an intuitionistic fuzzy formal context is proposed, some properties are discussed. The constructive method of intuitionistic fuzzy concept lattice based on intuitionistic fuzzy logical operators is proposed, extension in-tension intuitionistic fuzzy operator and intension extension intuitionistic fuzzy operator are defined by intuitionistic fuzzy logical operators. Some properties of these operators are dis-cussed, and the equivalent conditions of these operators are presented. Attribute reduction of intuitionistic fuzzy concept lattice is studied. By using of the cuts of intuitionistic fuzzy sets, discernibility matrix is proposed, thus the method of attribute reduction of intuitionistic fuzzy concept lattice is established. |
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