Study On Structer And Constructing Algorithms Of Concept Lattice

Concept lattice is a hierarchical structure of concepts defined by a binary relation, as a tool for data analysis and rule extraction, which has inspired intensive research in both theory and applications. Concept lattice is needed to build from the context in the process of the application, therefore, the efficiency of constructing algorithm is very important. So after some properties of concept lattice were studied, the constructing algorithms of concept lattice were researched in this paper;at the same time, fuzzy concept lattice and its constructing algorithm were also described. The work is mainly the following:1. Properties of concept lattice and its Hasse diagram were studied.2. A lattice-constructing algorithm of fuzzy concept lattice was established. On the basis of the fuzzy concept lattice, some properties of fuzzy objects mapping and fuzzy attributes mapping were discussed, the corresponding membership functions were defined respectively;at the same time, a constructing algorithm of fuzzy concept lattice was given based on cut set of fuzzy relation by introducing relevant degree.3. A vertical union algorithm of concept lattice was discussed. Based on the apposition and subposition of contexts, the vertical union operation of contexts and concepts with the same attributes set were defined;secondly it was proved that the formed concept lattice of subcontexts vertically combined was the same to the vertical union of sublattices of these subcontexts. Finally, in combination with the ordered concept lattice defined, a union algorithm of concept lattices with the same attributes set was presented, meanwhile, the Hasse diagram was formed and a example was given.4. A decomposition algorithm of concept lattice was discussed. From the definition of decomposition function, the algorithm of one concept lattice decomposed into sublattices with the same attributes set was researched. Firstly,the decomposition function φ was defined, it was proved that when all the nodes of the concept lattice were sequenced by increasing order of the extent sizes,, thenode of the sublattice was formed and its intent was equal to the intent of the node decomposed if the extent decomposed by q> was formed for the first time;thenthe algorithm of decomposing a concept lattice into two sublattices with the same attributes set was presented;secondly the relation between the nodes of the concept lattice and of the sublattices was researched;then an example was given to demonstrate the algorithm;finally it was expressed that the vertical union operation is a counter operation of the decomposition function.