Before building interval concept lattice from the formal context, the interval parameters[ α, β] should be determined, which influence the concept extension, the lattice structure and the quantity and precision of extracted association rules. In order to obtain α and β with the biggest compression degree of interval concept lattice, firstly the definition of the similarity of binary relation pairs and covering-neighborhood-space from formal context were proposed, the similarity matrix of binary relation pairs was obtained, and the neighborhood of binary relation pairs was calculated by the covering which was obtained by similar class of γ. Secondly, update algorithm of concept sets based on change of parameters was raised, where concept sets were got on the basis of the non-reconstruction. Combining with covering-neighborhood of binary relation pairs on changing interval parameters, further the model of parameter optimization of interval concept lattice could be built based on compression theory. According to the size of the compression degree and its changing trend, the optimal values of interval parameters were found. Finally, the validity of the model was demonstrated by an example.

To solve the practical problem that some rules may be lost when the association rules are extracted directly after the construction of interval concept lattice for the different formal context, the different interval concept lattices must be merged firstly. To improve the efficiency of lattice generating and consolidation, the incremental generation algorithm of interval concept lattice should be improved firstly, and then the concepts were stored in the form of structures which were divided into existence concepts, redundancy concepts and empty concepts. Secondly, the binary relation between extension and intension was analyzed and the sufficient condition of vertical merger, consistency of interval concept lattice, was defined. Thirdly the concepts which have consistent intension were divided into six kinds after merging and the corresponding decision theorem was given. In the end, based on the principle of breadth-first, a new vertical integration algorithm was designed through the type judgment and different processing methods of the concept lattice nodes in the original interval concept lattice. Finally, an application example verified the effectiveness and efficiency of the algorithm.