Time series classification is one of the most studied theoretical and applied fields of time series analysis. Many classical machine learning as well as deep learning algorithms, have been developed during the last decade to accurately perform time series classification. However, the case where the time series are uncertain is still under-explored. In this work, we discuss the importance of uncertainty handling in machine learning in general and in time series classification in particular. We propose efficient, robust and explainable methods for the classification of uncertain time series. We assess our methods on simulated datasets, but also on a real scenario in the astrophysics in which uncertainty in preponderant. The results we obtained are understandable and trustable by astronomers. Our proposed methods are tools that will facilitate the understanding of the universe in which we life in particular, and the field of uncertain time classification in general.