## 4 Discussion  
We have developed and validated a novel artificial intelligence method called the GLCM-based FBLS, which combines gray-level co-occurrence matrix with fuzzy BLS. This method considers the texture information of X-ray images and utilizes fuzzy systems to enhance the robustness of the BLS model. Our experimental results demonstrate that this method is effective and efficient in detecting osteoporosis and osteopenia.  
Osteoporosis is a significant concern for athletes as it can have a detrimental impact on their health and athletic performance. It can lead to weakened bones and increased susceptibility to fractures, which can hinder an athlete's ability to train and compete. Currently, conventional screening strategies for osteoporosis, such as calcaneal quantitative ultrasonography (QUS), quantitative computed tomography (QCT), and magnetic resonance imaging (MRI) [45], are not widely used due to limitations such as high radiation doses and complex post-processing. This makes it challenging to incorporate these strategies into regular screening for athletes. Opportunistic osteoporosis screening using machine learning models based on X-ray images may be a more efficient approach, as X-ray images are widely available for training the model. Previous studies have applied various machine learning models to analyze, predict, and diagnose osteoporosis and osteopenia. Deep learning algorithms have also been utilized, achieving significant progress in the detection of osteoporosis. However, these deep learning methods are computationally intensive and lack interpretability.  
In contrast, our proposed GLCM-based FBLS method offers advantages in terms of its lightweight nature and ease of training compared to deep learning models. By utilizing the GLCM-based feature extraction method, complex information in images can be transformed into texture information, resulting in reduced noise. The incorporation of fuzzy systems in the FBLS allows for handling uncertainty and imprecision in data, resulting in robust and reliable results. Our experimental results demonstrate that our method outperforms traditional CNN models on various indices. Therefore, our proposed model shows promise in achieving more accurate and reliable results in osteoporosis screening for athletes, particularly in determining the presence of the disease. Additionally, the lightweight nature of our model enhances its portability and eliminates the need for storing a large number of parameters and features. Moreover, our model enables fast and accurate predictions directly from X-ray images, offering potential for integration with the daily examination of athletes.  
However, our study has several limitations that should be acknowledged. Firstly, it was a retrospective study with a relatively small sample size. Future prospective studies are needed to validate the generalization ability of the BLS model. Secondly, our study focused on a classification task rather than a regression task, aiming to predict BMD T-scores categories rather than exact values. This decision was made due to the complex non-linear relationship between knee bones and BMD T-scores, which poses challenges for regression modeling. Thirdly, to apply the proposed method to real-world scenarios, adjustments may be necessary in the fuzzy rules used in the FBLS algorithm to enhance its performance. Lastly, we did not evaluate the potential contribution of clinical factors, such as age and body mass index, to the AI models. Although a recent study found that demographic characteristics did not significantly improve the sensitivity of osteoporosis identification,another study suggested that biochemical indicators could enhance the accuracy of an image-based model.