Attribute Reduction Of Strongly Harmonious Decision Formal Context

Attribute reduction is an important direction in formal concept analysis. After attribute reduction, the formal context can reduce the interference of redundant attributes to the data analysis based on the original information, which makes the expression of knowledge more easily. Depending on whether there is a decision attribute in the formal context, formal context is divided into general formal context and decision formal context.In the decision formal context, it is divided into strong consistent decision formal context.and weak consistent decision formal context.. In this paper, we mainly study the attribute reduction in the strong consistent decision formal context.First of all, In order to get the reduction set of a strong harmonious decision formal context, this paper designs a method of attribute reduction based on improved discernibility matrix and discernibility function.In constructing the improved discernibility attribute matrix only needs to calculate difference sets between the concept in sub-context which is corresponding to the attributes concept in sub-context and its super concept.This method can avoid constructing the concept lattice before constructing the identification attribute matrix.the time complexity and space complexity of the algorithm can be effectively reduced.Secondly, for a single reduction of a strongly harmonious decision formal context, in terms of attribute importance under the same condition, this paper designs a heuristic attribute reduction method.The algorithm is built on the relationship between super and sub-attributes, can quickly identify whether a attribute is redundant in the current consistent set, identify the attributes of condition attributes and delete redundant attributes,the consistent set is changed to a reduction of the background.The algorithm does not need to construct the concept lattice and the paradigm shift,has obvious advantages in the process of solving the single reduction.Finally, the attribute importance degree is introduced to the condition attribute set,due to the different properties of different importance degree, resulting in the user in the face of different reduction will be preferred, so in all of reduction of a formal context isbound to have a reduction is optimal.In order to get the optimal reduction of a strong harmonious decision formal context,this paper also designs an improved attribute reduction algorithm based on the improved identification attribute matrix.Compared with the first method, this method can satisfy the requirement of reduction and avoid the paradigm shift of the identification function. The feasibility and effectiveness of the method is verified by an example in this paper.