Computer applications in non-traditional areas have put requirements on conceptual data modeling. Some conceptual data models, being the tool of design databases, have been proposed. However, information in real-world applications is often vague or ambiguous. Currently, less research has been done in modeling imprecision and uncertainty in conceptual data models and the design of databases with imprecision and uncertainty. In this chapter, a different level of fuzziness based on fuzzy set and possibility distribution theory will be introduced into the IFO data model and the corresponding graphical representations will be given. The IFO data model is then extended to a fuzzy IFO data model, denoted IF2O. In particular, we provide the approach to mapping an IF2O model to a fuzzy relational database schema.