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Matrix Norm Minimization in Fuzzy Integrals: Optimization Methods for Choquet and Sugeno Measures |
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PP: 503-516 |
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doi:10.18576/amis/200216
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Author(s) |
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Yogeesh Nijalingappa,
Sulieman Ibrahim Mohammad,
Asokan Vasudevan,
Raja Natarajan,
Mohammed El Khiderauthor,
Poornachandran William,
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Abstract |
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| Fuzzy measures and their corresponding integrals (e.g., Choquet and Sugeno) play a pivotal role in non-additive aggregation within multi-criteria decision-making, data fusion, and complex decision analysis. This study proposes a matrix norm minimization framework to systematically learn fuzzy measures while controlling model complexity and enhancing interpretability. By representing fuzzy measure parameters in matrix form, we exploit well-established linear algebra and optimization techniques—such as l1,l2, or nuclear norm regularization—to impose sparsity, smoothness, or low-rank structure on the measure. We detail the formulation, theoretical properties, and step-by-step iterative algorithms (e.g., projected gradient and proximal methods) needed to handle both Choquet and Sugeno integrals. Experimental evaluations on synthetic and real-type datasets demonstrate significant improvements in measure accuracy, robustness to noise, and interpretability over baseline methods without regularization. Furthermore, we highlight potential extensions to larger-scale problems, non-convex integrals, and the integration of fuzzy measures with machine learning frameworks. These contributions unify fuzzy measure theory with modern optimization paradigms, opening new avenues for flexible, scalable, and insightful non-additive aggregation models in decision science and beyond. |
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