Fang ZhiXin, Yao XinLi, Song Man
Physical Education, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
Cangzhou Normal College, Education, Cangzhou, 061001, China.
Sci Rep. 2025 Jul 22;15(1):26678. doi: 10.1038/s41598-025-08605-y.
In the highly competitive world of modern football, each millisecond and centimeter can influence match outcomes. A team's overall performance often hinges on the positioning and movement of even a single player. Thus, the positioning of each player according to his skill set is crucial to enhance overall performance. This study develops a mathematical model that optimizes player positioning for a football team, considering key attributes such as technical awareness and decision-making, stamina and endurance, ball control and passing (technical ability), coordination, and communication. The combined composite solution (COCOSO) and circular intuitionistic fuzzy set (CrIFS) consider the factors affecting the player's performance. Furthermore, a data aggregation model based on the weighted averaging mean and weighted geometric mean is developed using the Einstein t-norm (ETN) and the Einstein t-conorm (ETCN). The developed model aggregates the data collected, integrating the COCOSO method. The resulting aggregation operators (AOs) are examined for their fundamental properties and then used in conjunction with COCOSO to identify the most suitable player positions, balancing individual strengths and weaknesses. A comparative analysis confirms that the proposed AOs offer noticeable advantages over existing aggregation techniques, underscoring the practical significance of the model.
在现代足球竞争激烈的世界中，每一毫秒和每一厘米都可能影响比赛结果。一支球队的整体表现往往甚至取决于一名球员的位置和移动。因此，根据球员的技能组合来确定每个球员的位置对于提高整体表现至关重要。本研究开发了一个数学模型，该模型考虑技术意识和决策、耐力和持久力、控球和传球（技术能力）、协调性和沟通等关键属性，为一支足球队优化球员位置。组合复合解（COCOSO）和循环直觉模糊集（CrIFS）考虑了影响球员表现的因素。此外，使用爱因斯坦t - 范数（ETN）和爱因斯坦t - 余范数（ETCN）开发了一种基于加权平均均值和加权几何均值的数据聚合模型。所开发的模型聚合收集到的数据，并结合COCOSO方法。对所得的聚合算子（AO）进行基本性质检验，然后与COCOSO结合使用，以确定最合适的球员位置，平衡个人的优势和劣势。对比分析证实，所提出的AO相对于现有聚合技术具有显著优势，突出了该模型的实际意义。
