The article addresses the challenge of scheduling construction projects given the considerable uncertainty associated with project time estimation. A fuzzy approach, which allows for modelling uncertainty, is employed to represent the duration of project tasks. It is shown, however, that the most well-known fuzzy numbers do not encompass all aspects of uncertainty. This study thus introduces a novel application of a specific type of fuzzy numbers, the Z*-numbers, which allow for the consideration of several factors that strongly influence the estimation process, including individual human characteristics, experience, and the project and task context. The underlying theory is discussed, and its application to the scheduling of construction projects is proposed. The approach and its benefits are demonstrated through a practical example involving the construction of a single-family house. Advantages include a more credible and accurate estimation of task durations that accounts for uncertainty while mitigating subjective, individual, and context-dependent elements. Further research perspectives are also outlined.