Systematic generation method and efficient representation of proximity relations for fuzzy relational database systems

One of the obstacles to building practical fuzzy database systems is to acquire semantic data such a proximity relation. The proximity relation is represented by the degree of `closeness´ or `similarity´ between data objects of a scalar domain. A fuzzy database system evaluates imprecise queries with the proximity relations. A systematic method to generate degrees of proximity and efficient representations of the proximity relation are proposed. The proposed generation method is simple and systematic. It is based on the well-known fuzzy set theory and applicable to real world applications because it has a tuning parameter. The proposed representations of proximity relation are more efficient than the ordinary matrix representation since they reflect some properties of a proximity relation to save space. We show an example of quantitative calculation for the proximity relation. And we analyze the time complexity and the space occupancy of the proposed representation methods