The importance of public stadiums has become increasingly prominent, but the efficiency of its performance management operation mechanism is low, which affects the overall operation efficiency of the whole stadium. However, due to the diversity and incompleteness of its data types, the traditional analytic hierarchy process is difficult to construct its index system. This article introduces the grey fuzzy analytic hierarchy process. Based on the analysis of its performance management problems, this article constructs the index system and makes an application case analysis. The results show that the GFAHP method (group fuzzy analytic hierarchy process) can ensure the integrity of information data. In data classification, the highest accuracy of sample classification is 40.13%, and the relative error rate is basically less than 6%. The performance effect is much higher than other classification algorithms. At the same time, the total score of the evaluation index system constructed by GFAHP is more than 3, the overall operation is good, and the risk evaluation effect of each influencing index factor is also good. Using the grey analytic hierarchy process to evaluate the operation and performance management of public stadiums and gymnasiums will help managers do a good job in risk control and quality dynamic adjustment, so as to improve the operation efficiency and benefit of stadiums and gymnasiums.

Gymnastics is an increasingly popular sport and an important event in the Olympic Games. However, the number of unavoidable injuries in sports is also increasing, and the treatment after the injury is very important. We reduce the harm caused by the injury through the identification and research of pictures. Image preprocessing and other methods can in-depth learn about gymnastics sports injuries. We identify the injured pictures of athletes to know the injury situation. Through the analysis of the force of the athletes during exercise, they can be better integrated into picture recognition for sports injuries. More appropriate prevention and treatment measures are suggested.