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

Proximity-based equivalence classes in fuzzy relational database model