| This paper arms to study the approximation of concept’s extension and concept representation and extracting concept lattices on factor data bases based on the factor spaces theory.As to some problems of the approximation representation of concept’s extension, two methods of the approximation, feedback extensions on single factor and envelopes of feedback extensions on multiple factors, are constructed by the feedback extension at the sight of the concept itself and its inverse concept, respectively. Then, its related properties are showed after some consistent relationships between this approximations and the counterparts in rough set are proved. The sufficient measure and important measure of single factor and multiple factors are defined based on the approximated level of the constructed approximations. As to the precision problems of the defined feedback extensions in approximating the concept extension are discussed and five improved methods are provided. Fuzzy decision-making based on the approximate extension of concept is studied. One inversing thinking decision-making is proposed and its effective and feasible are verified by an practical example.As to some problems of concept represention and extracting concept lattices, the formal definitions of concept are defined on the context piece of factor and concept analysis table, repectively. And some properties and algorithms of constructing concept lattice are provided. Here, reducing concept intention and concept lattice with reduced intention are proposed. And one algorithm used to extract the concept lattice with reduced intention on concept analysis table is also given. It follows from some examples that the concept lattice is not only simple and intuitive, but also has good fault tolerance and convenience in knowledge acquisition. Based on the idea of intension reducting, a polynomial algorithm is easly given for generating all concept extensions contained in a concept analysis table. |
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