Fuzzy relational databases: Representational issues and reduction using similarity measures

Until now, the idea of a fuzzy database has been investigated along different lines: Some authors have dealt with the imprecision of attribute values by modeling, using fuzzy similarity relations, the extent to which these values could be regarded as interchangeable. Others have used possibility distributions for representing fuzzily known or incompletely known attribute values. The first approach, which cannot accommodate incomplete information, is restated in the framework of rough sets extended to fuzzy relations. Besides, in the second one, similarity measures between attribute values can be introduced and computed; then a comparison of the two approaches is provided. The proposed similarity measure, based on a fuzzy Hausdorff distance, estimates the mismatch between two possibility distributions. From storage and query‐evaluation points of view, it may be interesting to gather items having similar attribute values. Thus the similarity measures previously considered can be used for the reduction of the fuzzy database. When several items have sufficiently similar values for each attribute in a relation, the reduction is performed by taking for each attribute the union of these similar values. The consequences of the reduction process on query evaluation are studied. © 1987 John Wiley & Sons, Inc.