Temporal data (TD) in Semantic Web are affected by different types of imperfections principally conflict. In the literature, most of the proposed approaches deal with perfect TD. However, to our knowledge, there is no approach to dealing with conflicting TD. In this paper, we propose an approach to represent and reason about quantitative conflicting TD (i.e., time intervals and points) and associated qualitative relations (e.g., “before”). This approach is based on evidence theory and it is three folds. (i) For the representation, the mass function of the conflicting temporal data is estimated, through the believability measures estimated based on our previous DBE_ALZ approach. Then, an ontology-based representation for the handled TD associated with the obtained mass function is proposed. (ii) For the reasoning, our approach relies on the Allen’s interval relations. First, we extend this algebra to reason about conflicting temporal relations. The resulting interval relations preserve the properties of the original algebra. Second, we adapt the proposed relations to define new ones relating a time interval and a time point, and two time points. All the proposed relations can be used for temporal reasoning through transitivity tables. (iii) Based on (i) and (ii), we propose a new evidential ontology named “BeliefTimeOnto”. We implement a prototype to ease the interaction with the proposed ontology. We conduct two case studies: the first is about temporal data entered by Alzheimer’s patients in the context of a memory prosthesis and the second is about data entered the context of Collective Memory application. The evaluation proves the usefulness of the proposed approach as all the inferences are well established and the precision results are interesting.