Databases available from many industrial or research fields are often imperfect. In particular, they are most of the time incomplete in the sense that some of the values are missing. When facing this kind of imperfect data, two techniques can be investigated: either using only the available information or estimating the missing values. In this paper we propose an estimation-based approach for sequence mining. This approach considers partial inclusion of an item within a record using fuzzy sets. Experiments run on various synthetic datasets show the feasibility and validity of our proposal as well in terms of quality as in terms of the robustness to the rate of missing values.