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    Local Boundary Fuzzified Rough K-Means-Based Information Granulation Algorithm Under the Principle of Justifiable Granularity
    (Ieee-Inst Electrical Electronics Engineers Inc, 2024) Zhang, Tengfei; Zhang, Yudi; Ma, Fumin; Peng, Chen; Yue, Dong; Pedrycz, Witold
    Information granularity and information granules are fundamental concepts that permeate the entire area of granular computing. With this regard, the principle of justifiable granularity was proposed by Pedrycz, and subsequently a general two-phase framework of designing information granules based on Fuzzy C-means clustering was successfully developed. This design process leads to information granules that are likely to intersect each other in substantially overlapping clusters, which inevitably leads to some ambiguity and misperception as well as loss of semantic clarity of information granules. This limitation is largely due to imprecise description of boundary-overlapping data in the existing algorithms. To address this issue, the rough k-means clustering is introduced in an innovative way into Pedrycz's two-phase information granulation framework, together with the proposed local boundary fuzzy metric. To further strengthen the characteristics of support and inhibition of boundary-overlapping data, an augmented parametric version of the principle is refined. On this basis, a local boundary fuzzified rough k-means-based information granulation algorithm is developed. In this manner, the generated granules are unique and representative whilst ensuring clearer boundaries. The validity and performance of this algorithm are demonstrated through the results of comparative experiments.
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    Rough fuzzy k-means clustering based on parametric decision-theoretic shadowed set with three-way approximation
    (Springer, 2024) Zhang, Yudi; Zhang, Tengfei; Peng, Chen; Ma, Fumin
    Rough fuzzy K-means (RFKM) decomposes data into clusters using partial memberships by underlying structure of incomplete information, which emphasizes the uncertainty of objects located in cluster boundary. In this scheme, the settings of cluster boundary merely depend on subjective judgment of perceptual experience. When confronted with the data exhibiting heavily overlap and imbalance, the boundary regions obtained by existing empirical schemes vary greatly accompanied by skewing of cluster center, which exerts considerable influence on the accuracy and stability of RFKM. This paper seeks to analyze and address this deficiency and then proposes an improved rough fuzzy K-means clustering based on parametric decision-theoretic shadowed set (RFKM-DTSS). Three-way approximation is implemented by incorporating a novel fuzzy entropy into the decision-theoretic shadowed set, which rationalizes cluster boundary through minimizing fuzzy entropy loss. Under the secondary adjustment method and improved update strategy of cluster center, the proposed RFKM-DTSS is thus featured by a powerful processing ability on class overlap and imbalance commonly seen in scenarios, such as fault detection and medical diagnosis with unclear decision boundaries. The effectiveness and robustness of the RFKM-DTSS are verified by the results of comparative experiments, demonstrating the superiority of the proposed algorithm.