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While various articles about fuzzy entity relationship (ER) and enhanced entity relationship (EER) models have recently been published, not all examine how the constraints expressed in the model may be relaxed. In this paper, our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool, so that these constraints can be made more flexible. We will also study new constraints that are not considered in classic EER models. We use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases. In addition, we shall examine the representation of these constraints in an EER model and their practical repercussions. The following constraints are studied: the fuzzy participation constraint, the fuzzy cardinality constraint, the fuzzy completeness constraint to represent classes and subclasses, the fuzzy cardinality constraint on overlapping specializations, fuzzy disjoint and fuzzy overlapping constraints on specializations, fuzzy attribute-defined specializations, fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses. We shall also demonstrate how fuzzy (min, max) notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint. All these fuzzy constraints have a new meaning, they offer greater expressiveness in conceptual design, and are included in the so-called fuzzy EER model.