  One of the first attempts to set a solid theoretical foundation for extending
the content of relational databases with incomplete information was the fuzzy
relational model by Buckles and Petry. This structure was based on two
generalizations of the traditional relational model: (1) A tuple component can
be any subset of the corresponding domain, rather than a single element and (2)
A similarity relation is defined on each domain. This relation satisfies the
properties of reflexivity, symmetry and max-min transitivity, thus having the
equality relation as a special case. This generalization keeps two key
properties of the relational model - that no two different tuples represent the
same information and that the application of any operation of the relation
algebra has a unique result.
  Shenoi and Melton generalized this model and showed how the existence of
equivalence classes over the attribute domains can also be preserved with a
relation that only satisfies the properties of reflexivity and symmetry
(proximity relation). The motivation for this generalization is the strictness
of the max-min transitivity property of similarity relations, which complicates
the construction of this relation for some domain types.
  An important characteristic of the Shenoi-Melton model is the dependence of
the equivalence classes upon the current content of the database. This
characteristic, together with the way the equivalence relation is constructed
by the proximity relation, can lead to the equivalence classes that don't
correspond well with some database query types.
  Here we will present a different way of forming the equivalence classes over
the attribute domains in fuzzy relational databases in which they depend only
on the attribute domain and not on the current database state. We will also
show a simple method for automatic construction of proximity relations over
some domain types.
