Similarity measures of double-valued neutrosophic sets based on cotangent function and applications to football players' competitive ability evaluation

At present, China's football sports are relatively backward in training theory and practice. If you want to break out of Asia and enter the world, and gain a firm foothold in the international football arena, you must use a scientific and realistic attitude, absorb the successful experience of advanced football countries, reflect on our training concepts and practices, and deeply study the training laws of football, in order to find a way suitable for our development. Athletes' competitive ability is the core issue of sports training. The failure of our football level is directly related to our systematic understanding of athletes' competitive ability. This problem has led to the separation of our training practice from the actual competition, making training unable to meet the needs of the competition. Only by solving this problem, can we improve the level of football in China. The football players' competitive ability evaluation is affirmed as multiple attribute decision making (MADM). In such paper, motivated by the idea of cotangent similarity measure (CSM), the CSMs are extended to DVNSs and four CSMs are created under DVNSs. Then, two weighted CSMs are built for MADM under DVNSs. Finally, a numerical example for Football players' competitive ability evaluation is affirmed and some comparative algorithms are produced to affirm the built method.