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