Explainable granular fusion: Graph-embedded rectangular neighborhood rough sets for knowledge system convergence

With the development of Rough Set Theory (RST), many improved theories based on RST have emerged. Some of these theories have been applied in the field of feature selection, significantly improving its efficiency. However, they have not yet been widely used in multi-source information domains. This paper proposes a multi-source information fusion method based on Granular-Rectangular Neighborhood Rough Set (GRNRS) and graph theory. First, an improved algorithm based on GRNRS is proposed to evaluate the contribution of each information source to a classification task under a specific attribute. In this process, we provided rigorous theoretical proofs for the concepts and mechanisms used in the improved GRNRS. Meanwhile, the Pearson Correlation Coefficient (PCC) is used to assess the linear relationship between information sources. Then, by integrating the results of the improved GRNRS algorithm and PCC, the adjacency matrix of a graph is constructed. Finally, the preference value of each information source under a specific attribute is calculated based on the adjacency matrix. Information fusion under a specific attribute is achieved by selecting the information source with the highest preference value. Extensive experiments are conducted to analyze the impact of the algorithm's parameters on its final performance. Meanwhile, our method is compared with seven other information fusion algorithms using three metrics: classification accuracy, Average Quality (AQ), and runtime. Friedman and Nemenyi tests are conducted on the comparison results under the classification accuracy and AQ metrics, demonstrating that there are significant differences among the algorithms. The results demonstrate that the proposed algorithm is both time-efficient and effective.