Temporal representation and reasoning are important facets in the design of many Semantic Web applications. Several approaches exist to represent and reason about precise temporal data in ontology. However, most of them handle only time intervals and associated qualitative relations. Besides, to the best of our knowledge, there is no approach devoted to handle imprecise temporal data (e.g., “late 1970s”). In this paper, we propose an ontology-based approach for representing and reasoning about precise and imprecise temporal data. Quantitative temporal data (i.e., time intervals and points) and qualitative ones (i.e., relations between time intervals, relations between a time interval and a time point and relations between time points) are taken into consideration. Our approach is three folds: (i) extending the 4D-fluents approach with new crisp and fuzzy components, to represent precise and imprecise temporal data, (ii) extending the Allen’s interval algebra to enable reasoning about precise and imprecise temporal data, and (iii) creating a Fuzzy-OWL 2 ontology TimeOnto that, based on the extended Allen’s interval algebra, instantiates our 4D-fluents-based representation. The extension that we propose for the Allen’s interval algebra handles precise and imprecise time intervals. Indeed, it enables expressing precise (e.g., “before”) and imprecise (e.g., “just before”) temporal relations. Compared to related work, our imprecise relations are personalized, in the sense that they are not limited to a defined set of interval relations and their meanings are determined by the domain expert. For instance, the classic Allen’s relation “Before” may be generalized in 5 imprecise relations, where “Before(1)” means “just before” and gradually the time gap between the two intervals increases until “Before(5)” which means “very long before”. To enable this representation, we propose an extension of the Vilain and Kautz’s point algebra and redefined the Allen’s relations by means of this extended algebra. We show in this paper that, unlike most related work, the resulting relations preserve many of the desirable properties of the Allen’s interval algebra. The definitions of the resulting interval relations are adapted to allow relating a time interval and a time point, and two time points, where time intervals and points maybe both precise or both imprecise. These relations can be used for temporal reasoning by means of four transitivity tables. Finally, we describe a prototype based on “TimeOnto” that infers new relations using a set of SWRL and fuzzy IF-THEN rules. This prototype was integrated in an ontology-based memory prosthesis for Alzheimer’s patients.