In this article our aim is to relax the constraints which can be expressed in a conceptual model using the Enhanced Entity Relationship modeling tool, so that these constraints can be made more flexible. To do so we will use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and of fuzzy consultation systems for databases. We will also examine the representation of these constraints in an EER model and their practical repercussions. The constraints proposed are as follows: fuzzy participation constraint, fuzzy cardinality constraint, fuzzy completeness constraint in the representation of classes, sub-classes (and categories or union types) and fuzzy cardinality constraint in overlapping specialization. We also demonstrate how fuzzy (min, max) notation can substitute fuzzy cardinality constraint. All these fuzzy constraints have a novel meaning and offer greater expressiveness in conceptual design.