Conditional functional dependencies (CFDs) have been used to improve the quality of data, including detecting and repairing data inconsistencies. Approximation measures have significant importance for data dependencies in data mining. To adapt to exceptions in real data, the measures are used to relax the strictness of CFDs for more generalized dependencies, called approximate conditional functional dependencies (ACFDs). This paper analyzes the weaknesses of dependency degree, confidence and conviction measures for general CFDs (constant and variable CFDs). A new measure for general CFDs based on incomplete knowledge granularity is proposed to measure the approximation of these dependencies as well as the distribution of data tuples into the conditional equivalence classes. Finally, the effectiveness of stripped conditional partitions and this new measure are evaluated on synthetic and real data sets. These results are important to the study of theory of approximation dependencies and improvement of discovery algorithms of CFDs and ACFDs
