The Discussion Of L-Fuzzy Rough Sets

Rough set is a mathematic tool to descript the uncertainty information. The theory can analysis the uncompleted, unconsist information, and discover the hidden knowledge and rules.As the extension of fuzzy rough set model, L-fuzzy rough set can describe not only the fuzziness and uncompletement, but also the uncomparability in the information systems. As Boolean algebra and residuated lattice replace the interval [0, 1] in L-fuzzy rough set, the properties of the lower and upper approximation operators have been changed. The changes open out the relations between basis algebra, binary relation and the lower and upper approximation operators in the rough set. Following the former methods of studying approximation operators in rough set, this paper will discuss the L-fuzzy rough set model in the constructive approach and the axiomatic approach. The concrete work in this paper shows as follows.Part one is chapter two. In this part, we discuss the properties of lower and upper approximation operators of L-fuzzy rough set based on Boolean algebra and the axiomatic approach of the lower and upper approximation operators based on Boolean algebra.In part two, the discussion centers on the relations of three elements in rough set which are the binary relations in universe, basis algebra and the lower and upper approximation operator. This part can be divided into three sub-parts, which are chapter three, chapter four and chapter five. In chapter three, we discuss the properties of L-fuzzy rough lower and upper approximation operators based on different algebras (such as: residuated lattice, MTL algebra, IMTL algebra and lattice implication algebra), different binary relation (such as: serial, reflexive, symmetry, (?) -transitive, L-fuzzy similar and L-fuzzy equivelant) and different forms of approximation operator. The differences of approximation operators' properties manifest the fact which basis algebra and binary relation decide to the properties of the approxiomation operators. In thapter four, we discuss the axiomatic approach of approximation operator based on different basis algebras (such as residuated lattice and IMTL algebra) and different properties of approximation operators. That represents the constraint relation which the basis algebra and approximation operator preporties influence the binary relation in axiomatic approach. Using the conclusion in axiomatic approach, we discuss the topology structure of rough approximation operator and study the relation between the approximation space and topological space. In chapter five, we discuss the fact which the approximation operator properties and binary relation influence the choice of basis algebra. Under the frame of basis algebra, we try to construct the form of approximation operator.As to the application of rough set, in the chapter five, At first, we introduce the Chinese text categorization system in [99]. we analyse the rule bank in the text categorization system. Through analyzing the characteristic of the system, we use the rough set theory to reduce the rule bank. The reduced rule rank is used in the original text categorization system. The accuracy rate of text categorization system has been improved in the same cases.