Knowledge Granularity Attribute Reduction Algorithm for Incomplete Systems in a Clustering Context

The phenomenon of missing data can be seen everywhere in reality. Most typical attribute reduction models are only suitable for complete systems. But for incomplete systems, we cannot obtain the effective reduction rules. Even if there are a few reduction approaches, the classification accuracy of their reduction sets still needs to be improved. In order to overcome these shortcomings, this paper first defines the similarities of intra-cluster objects and inter-cluster objects based on the tolerance principle and the mechanism of knowledge granularity. Secondly, attributes are selected on the principle that the similarity of inter-cluster objects is small and the similarity of intra-cluster objects is large, and then the knowledge granularity attribute model is proposed under the background of clustering; then, the IKAR algorithm program is designed. Finally, a series of comparative experiments about reduction size, running time, and classification accuracy are conducted with twelve UCI datasets to evaluate the performance of IKAR algorithms; then, the stability of the Friedman test and Bonferroni–Dunn tests are conducted. The experimental results indicate that the proposed algorithms are efficient and feasible.