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<p>The rural population constitutes a significant portion of China’s total population, and enhancing their physical fitness is crucial to raising the overall fitness level across the nation. Gaining insights into public sports services for the elderly in rural areas is essential for analyzing the current state of the service system and its underlying context, with the goal of proposing strategies to optimize these services. This involves improving the rural sports and fitness service system for elderly people by considering various aspects such as policies, regulations, funding sources, and outreach efforts, ultimately enhancing their quality of life and physical fitness. The evaluation of demand for public sports services for rural elderly can be approached through multiple-attribute group decision-making (MAGDM). Spherical fuzzy sets (SFSs) offer a more effective and comprehensive means to address the uncertainty and vagueness in assessing this demand. In this study, a bidirectional projection method is introduced, along with the spherical fuzzy bidirectional projection (SFBP) technique and spherical fuzzy weighted bidirectional projection (SFWBP) technique. Using the developed SFWBP technique, the MAGDM framework is structured, and all computational steps are outlined. To validate the SFWBP technique, a numerical example focused on the demand evaluation for rural elderly sports services is provided, accompanied by comparative analyses that demonstrate the advantages of the SFWBP technique within the context of SFSs. The key contributions of this research can be summarized: (1) the Method Based on the Removal Effects of Criteria (MEREC) method is applied to determine weight values; (2) bidirectional projection (BP) techniques are extended to SFSs; (3) several BP techniques integrated with SFSs are developed to handle MAGDM scenarios; and (4) a numerical case study is conducted to implement SFWBP techniques with SFSs, while comparative analyses are carried out to confirm the superiority of the SFWBP technique.</p>

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Modified Bidirectional Projection Technique for Spherical Fuzzy MAGDM and Applications to Demand Evaluation for Public Sports Services for the Elderly in Rural Areas

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Sen Wang,
  • Jie Wang,
  • Yanan Qiao,
  • Ruohan Zhang

摘要

The rural population constitutes a significant portion of China’s total population, and enhancing their physical fitness is crucial to raising the overall fitness level across the nation. Gaining insights into public sports services for the elderly in rural areas is essential for analyzing the current state of the service system and its underlying context, with the goal of proposing strategies to optimize these services. This involves improving the rural sports and fitness service system for elderly people by considering various aspects such as policies, regulations, funding sources, and outreach efforts, ultimately enhancing their quality of life and physical fitness. The evaluation of demand for public sports services for rural elderly can be approached through multiple-attribute group decision-making (MAGDM). Spherical fuzzy sets (SFSs) offer a more effective and comprehensive means to address the uncertainty and vagueness in assessing this demand. In this study, a bidirectional projection method is introduced, along with the spherical fuzzy bidirectional projection (SFBP) technique and spherical fuzzy weighted bidirectional projection (SFWBP) technique. Using the developed SFWBP technique, the MAGDM framework is structured, and all computational steps are outlined. To validate the SFWBP technique, a numerical example focused on the demand evaluation for rural elderly sports services is provided, accompanied by comparative analyses that demonstrate the advantages of the SFWBP technique within the context of SFSs. The key contributions of this research can be summarized: (1) the Method Based on the Removal Effects of Criteria (MEREC) method is applied to determine weight values; (2) bidirectional projection (BP) techniques are extended to SFSs; (3) several BP techniques integrated with SFSs are developed to handle MAGDM scenarios; and (4) a numerical case study is conducted to implement SFWBP techniques with SFSs, while comparative analyses are carried out to confirm the superiority of the SFWBP technique.