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<p>This paper proposes an advanced decision-making framework grounded in novel Schweizer–Sklar-based aggregation operators for Fuzzy Bipolar Soft Sets (FBSS), aiming to overcome the inherent computational complexity and underutilization of FBSS in multi-criteria decision-making (MCDM) environments. Specifically, we introduce new Schweizer–Sklar operational laws tailored for FBSS values and construct four aggregation operators: FBSS Schweizer–Sklar Weighted Average (FBSSSWA), Ordered Weighted Average (FBSSSOWA), Weighted Geometric (FBSSSWG), and Ordered Weighted Geometric (FBSSSOWG). A normalized Hamming distance measure is incorporated to enhance the reliability and accuracy of the aggregation process. The proposed methodology is theoretically validated through an axiomatic analysis of the aggregation operators, and practically implemented in a multi-attribute decision-making (MADM) model. Empirical data were collected from publicly available benchmark repositories and peer-reviewed comparative studies involving four prominent deep learning architectures: Transformers, Deep Reinforcement Learning (DRL), Generative Adversarial Networks (GANs), and Convolutional Neural Networks (CNNs). These models were evaluated against four key performance criteria—scalability, adaptability, interpretability, and generalization identified through expert consultation and literature review. A comprehensive sensitivity analysis was conducted to examine the influence of the Schweizer–Sklar parameter on decision outcomes. Comparative evaluation reveals that the proposed framework surpasses traditional approaches in terms of robustness, computational efficiency, and decision consistency. The findings suggest that Schweizer–Sklar-based FBSS aggregation operators constitute a powerful and flexible tool for high-stakes model evaluation in artificial intelligence systems. This framework has potential policy implications for model selection, deployment, and governance in data-intensive domains such as healthcare, finance, and autonomous systems.</p>

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A novel Schweizer Sklar aggregation framework for fuzzy bipolar soft numbers in multi-criteria decision-making: application to deep learning model evaluation

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Zia Ullah,
  • Fazli Amin,
  • Marouan Kouki,
  • Hakim AL Garalleh,
  • Afnan Al Agha

摘要

This paper proposes an advanced decision-making framework grounded in novel Schweizer–Sklar-based aggregation operators for Fuzzy Bipolar Soft Sets (FBSS), aiming to overcome the inherent computational complexity and underutilization of FBSS in multi-criteria decision-making (MCDM) environments. Specifically, we introduce new Schweizer–Sklar operational laws tailored for FBSS values and construct four aggregation operators: FBSS Schweizer–Sklar Weighted Average (FBSSSWA), Ordered Weighted Average (FBSSSOWA), Weighted Geometric (FBSSSWG), and Ordered Weighted Geometric (FBSSSOWG). A normalized Hamming distance measure is incorporated to enhance the reliability and accuracy of the aggregation process. The proposed methodology is theoretically validated through an axiomatic analysis of the aggregation operators, and practically implemented in a multi-attribute decision-making (MADM) model. Empirical data were collected from publicly available benchmark repositories and peer-reviewed comparative studies involving four prominent deep learning architectures: Transformers, Deep Reinforcement Learning (DRL), Generative Adversarial Networks (GANs), and Convolutional Neural Networks (CNNs). These models were evaluated against four key performance criteria—scalability, adaptability, interpretability, and generalization identified through expert consultation and literature review. A comprehensive sensitivity analysis was conducted to examine the influence of the Schweizer–Sklar parameter on decision outcomes. Comparative evaluation reveals that the proposed framework surpasses traditional approaches in terms of robustness, computational efficiency, and decision consistency. The findings suggest that Schweizer–Sklar-based FBSS aggregation operators constitute a powerful and flexible tool for high-stakes model evaluation in artificial intelligence systems. This framework has potential policy implications for model selection, deployment, and governance in data-intensive domains such as healthcare, finance, and autonomous systems.