In this paper, we propose an ontology-based approach for representing and reasoning about precise and imprecise time intervals. This approach is three folds: (i) extending the 4D-fluents approach with new crisp and fuzzy components, to represent precise and imprecise time intervals, and temporal relations between them, (ii) extending the Allen's interval algebra to enable reasoning about the handled temporal data, and (iii) creating a Fuzzy-OWL 2 ontology "TimeOnto" that, based on the extended Allen's interval algebra, instantiate our 4D-fluents-based representation. The extension of the Allen's algebra handles precise and imprecise time intervals to express 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 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 "too long before". To enable this representation, we propose an extension of the Vilain and Kautz's point algebra and a redefinition of the Allen's relations by means of this extended algebra. Unlike most related work, the resulting relations preserve many of the desirable properties of the Allen's algebra. These relations can be used for temporal reasoning by means of a transitivity table. 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.