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Currently, density-based clustering algorithms are widely applied because they can detect clusters with arbitrary shapes. However, they perform poorly in measuring global density, determining reasonable cluster centers or structures, assigning samples accurately and handling data with large density differences among clusters. To overcome their drawbacks, this paper proposes a granule fusion density-based clustering with evidential reasoning (GFDC). Both local and global densities of samples are measured by a sparse degree metric first. Then information granules are generated in high-density and low-density regions, assisting in processing clusters with significant density differences. Further, three novel granule fusion strategies are utilized to combine granules into stable cluster structures, helping to detect clusters with arbitrary shapes. Finally, by an assignment method developed from Dempster-Shafer theory, unstable samples are assigned. After using GFDC, a reasonable clustering result and some identified outliers can be obtained. The experimental results on extensive datasets demonstrate the effectiveness of GFDC.

Three-way decision (3WD) is a powerful tool for granular computing to deal with uncertain data, commonly used in information systems, decision-making, and medical care. Three-way decision gets much research in traditional rough set models. However, three-way decision is rarely combined with the currently popular field of machine learning to expand its research. In this paper, three-way decision is connected with SVM, a standard binary classification model in machine learning, for solving imbalanced classification problems that SVM needs to improve. A new three-way fuzzy membership function and a new fuzzy twin support vector machine with three-way membership (TWFTSVM) are proposed. The new three-way fuzzy membership function is defined to increase the certainty of uncertain data in both input space and feature space, which assigns higher fuzzy membership to minority samples compared with majority samples. To evaluate the effectiveness of the proposed model, comparative experiments are designed for forty-seven different datasets with varying imbalance ratios. In addition, datasets with different imbalance ratios are derived from the same dataset to further assess the proposed model's performance. The results show that the proposed model significantly outperforms other traditional SVM-based methods.

In a dynamic environment, knowledge reduction of information systems with variations of object sets, attribute sets and attribute values is an important topic of rough set theory, and related family-based attribute reduction of dynamic covering information systems when refining and coarsening coverings has attracted little attention. In this paper, firstly, we introduce the concepts of the refinement and coarsening of a covering and provide the mechanisms of updating related families of dynamic covering decision information systems with refining and coarsening coverings. Meanwhile, we investigate how to construct attribute reducts with the updated related families and propose the incremental algorithms for computing attribute reducts of dynamic covering decision information systems. Finally, the experimental results verify that the proposed algorithms are more effective than the non-incremental algorithms for attribute reduction of dynamic covering decision information systems in terms of stability and computational time.