Chaoqian Li

The semi-supervised multiview clustering (MVC) methods based on non-negative matrix factorization (NMF) have attracted considerable attention due to their ability to utilize partial supervision information and significantly enhance clustering performance. Still, they often face challenges such as high computational costs and difficulties in parameter tuning. We propose a semi-supervised MVC method called Graph-Regularized and One-Hot-Constrained Symmetric NMF (MGOCS) to avoid these issues relatively. The key advantage of MGOCS includes the introduction of a parameter-free semi-supervised strategy that encodes partial label information as one-hot vectors during decomposition, the use of a shared consistency indicator matrix directly as the clustering assignment matrix for all views, and the incorporation of graph regularization terms for each view. These features effectively balance model complexity with information utilization. An iterative optimization algorithm is developed to solve MGOCS, accompanied by complexity and convergence analysis. Clustering experiments conducted on six multi-view datasets demonstrate that MGOCS outperforms various state-of-the-art methods in terms of clustering performance. The code is available at https://github.com/ljisxz/MGOCS.

In complex decision-making scenarios, such as smart city renewable energy project selection, decision-makers must contend with multi-dimensional uncertainty, conflicting expert opinions, and evolving temporal dynamics. This study introduces a novel Fractional q-Rung Orthopair Fuzzy Tensor (Fq-ROFT)-based group decision-making methodology that integrates the flexibility of q-rung orthopair fuzzy sets with tensorial representation and fractional-order dynamics. The proposed framework allows for the modeling of positive and negative membership degrees in a multi-dimensional, time-dependent structure while capturing memory effects inherent in expert evaluations. A detailed case study involving six renewable energy alternatives and six criteria demonstrates the method’s ability to aggregate expert opinions, compute fractional dynamic scores, and provide robust, reliable rankings. Comparative analysis with existing approaches, including classical q-ROFSs, intuitionistic fuzzy sets, and weighted sum methods, highlights the superior discriminative power, consistency, and dynamic sensitivity of the Fq-ROFT approach. Sensitivity analysis confirms the robustness of the top-ranked alternatives under variations in expert weights and fractional orders and membership perturbations. The study concludes by discussing the advantages, limitations, and future research directions of the proposed methodology, establishing Fq-ROFT as a powerful tool for dynamic, high-dimensional, and uncertain group decision-making applications.

Some new sufficient conditions ensuring that the $k$-subdirect sum of strictly diagonally dominant matrices and Nekrasov matrices is in the class of Nekrasov matrices are given. These sufficient conditions are different from those in [Electron. J. Linear Algebra, 38:339-346, 2022] and [Linear Multilinear Algebra, 64:208-218, 2016; 72:1044-1055, 2023]. In addition, some examples are given to illustrate the conditions presented.