Fuzzy Concept Lattice Of Attribute Reduction Theory And Methods

Formal concept analysis (FCA), also called the theory of concept lattices, was proposed firstly by Wille R. in 1982, in order to deal with the discovery, compositor and revelation of the concepts. In which, the structural model of concept lattice is the core of data structure, and it describes the relation between objects and attributes essentially. A concept lattice embodies generalization and specialization relationships between concepts, and the corresponding Hasse graph can realize the visualization of data. Therefore, FCA has become an efficient methodology for data analysis and knowledge discovery. It has been applied to a variety of fields, such as digital library, documentary index, software engineering, and knowledge discovery.Being a generalization of FCA, the theory of fuzzy concept lattices is a powerful tool to deal with uncertainty knowledge. In fuzzy concept lattices, the objects, attributes and relations are no longer crisp sets, they are fuzzy sets or L-fuzzy sets. This paper mainly studies attribute reduction in the L-fuzzy concept lattices proposed by Belohavek. The main achievements contained in this dissertation are as follows:1. we give a definition of granular and granular matrix of L-fuzzy formal context. And some properties have been obtained about granular and granular matrix.2. we give a definition of attribute reduction in L-fuzzy concept lattices, which maintains the structure of L-fuzzy concept lattices. Secondly, in order to avoid the problem that discernibility matrix is difficult to be created in L-fuzzy concept lattices, we introduce the other definition of attribute reduction that keeping the extension sets of meet-irreducible elements in L-fuzzy concept lat- tices. And then, we prove that these two reductions are equivalent.3. Using the granular matrix and meet-irreducible elements, we find the method of attribute reduction and the judgement theorems of attribute charac-teristics.