Extending the fuzzy database with fuzzy numbers

The fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete, finite universe. The model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra. Where equivalence is required in an ordinary relational database, similarity is employed in a fuzzy relational database. For discrete, finite universes, similarity between atomic elements is described via a fuzzy similarity relation with max-min transitivity. Two or more fuzzy numbers are defined to be α-similar if their union forms a continuous α-level set over the real line. This convention effects the partitioning of fuzzy number domains that is necessary to assure the well-definedness of the fuzzy relational algebra.