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Fuzzy Partitioning of Quantitative Attribute Domains by a Cluster Goodness Index

The problem of mining association rules for fuzzy quantitative items was introduced and an algorithm proposed in [7]. However, the algorithm assumes that fuzzy sets are given. In this paper we propose a method to find the fuzzy sets for each quantitative attribute in a database by using clustering techniques. We present a scheme for finding the optimal partitioning of a data set during the clustering process regardless of the clustering algorithm used. More specifically, we present an approach for evaluation of clustering partitions so as to find the best number of clusters for each specific data set. This is based on a goodness index, which assesses the most compact and well-separated clusters. We use these clusters to classify each quantitative attribute into fuzzy sets and define their membership functions. These steps are combined into a concise algorithm for finding the fuzzy sets. Finally, we describe the results of using this approach to generate association rules from a real-life dataset. The results show that a higher number of interesting rules can be discovered, compared to partitioning the attribute values into equal-sized sets.