Measures of dependency in metric decision systems and databases

Attribute dependencies play an essential role for the problem of attribute reduction in decision systems. Data dependencies, including Matching Dependencies (MDs) and Metric Functional Dependencies (MFDs) have been applied for data cleaning, duplication and violation detection in the data quality problem. Approximation measures are used to loosen the strictness of dependencies for a better adaptation with data in the real world. Therefore, this paper introduces metric rough sets and dependency measures for metric decision systems. These rough sets make a connection between the metric decision systems and databases that allows us to apply the dependency measures for MDs and MFDs. These results are important to develop the applications of rough sets and construct the algorithms for the attribute reduction and discovery of MDs and MFDs in the metric decision systems and databases.