Temporal data given by users are often imprecise. In this paper, we propose an approach to represent and reason about temporal relations between imprecise time intervals which are classical time intervals characterized by gradual beginnings and/or endings. It is mainly based on extending the Allen’s interval algebra. It is not only suitable to express precise temporal interval relations (e.g., “Before”) but also imprecise personalized ones (e.g., “Just Before”). Compared to related work, our imprecise relations are personalized, in the sense that they are not limited to a given number and their meanings are determined by a 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 “too long before”. Our imprecise personalized relations are based on our extension of the Vilain and Kautz’s point algebra. We showed that, unlike most related work, our temporal interval relations preserve many of the properties of the Allen’s interval algebra. Furthermore, we show how they can be used for temporal reasoning by means of a transitivity table. Finally, our approach is applied to the Semantic Web. We propose a fuzzy ontology-based prototype. Inferences are done via a set of SWRL and fuzzy IF-THEN rules. We illustrate the usefulness of our approach in the context of an ontology-based memory prosthesis for Alzheimer’s patients.