Much lately, a leveled fully homomorphic encryption scheme was proposed based on the Learning With Rounding (LWR) problem. The LWR problem is a variant of the Learning With Errors (LWE) problem, but it dispenses with the costly Gaussian noise sampling. Thus, compared with the existing LWE-based fully homomorphic encryption schemes, the proposed LWR-based fully homomorphic encryption scheme has much higher efficiency. But then, the user's evaluation key was needed to be obtained in the homomorphic evaluator of the proposed LWR-based fully homomorphic encryption scheme. Accordingly, a new leveled fully homomorphic encryption scheme was constructed based on the LWR problem, and the user's evaluation key was not needed to be obtained in the homomorphic evaluator of the new fully homomorphic encryption scheme. Since the new proposed fully homomorphic encryption scheme can be used to construct the schemes such as identity-based fully homomorphic encryption schemes, and attribute-based fully homomorphic encryption schemes, the new proposed scheme has wider application than the lately proposed LWR-based fully homomorphic encryption scheme.

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.