In the digital age, the rapid dissemination of false information on social networks presents certain societal challenges. Traditional detection methods have some limitations in handling data uncertainty and incompleteness common in social media environments. Therefore, this study proposes a grey relational clustering model, tentatively integrating content features, user behaviors, and propagation network features to better address data uncertainty and incompleteness. Preliminary comparative experiments with conventional machine learning and deep learning approaches indicate that our model maintains accuracy above 85% even when 30% of data is missing, and achieves an accuracy of 92% and an F1-score of 0.92 on complete datasets. Additionally, the model demonstrates certain advantages in computational efficiency, being approximately 2.5 times faster than traditional machine learning models and about 9 times faster than BERT. This research hopes to contribute modestly to real-time false information detection by providing a relatively efficient and somewhat adaptive analytical tool for social media environments.