2012 IEEE International Conference on Granular Computing Mining Associative Decision Rules in Decision Tables through Attribute Value Reduction Jianchao Han Department of Computer Science Califonia State University Dominguez Hills Carson, CA, USA jhan@csudh.edu Abstract- There are many algorithms and approaches developed to induce decision rules in decisio/information tables. Basically, these methods share a common idea: reduction, including row reduction, column reduction, and cell reduction. Most solutions based on the rough set theory integrate these three reductions in the above order, where column reduction is performed by inding attribute reducts and cell reduction is conducted via value reduction. Since there may exist various attribute reducs, many efforts have been put on seeking the best or optimal reduct in the sense of accurate decisions. However, different attribute reducts are only equivalent in the circumstance of the given decision table. The decision rules that are induced from different attribute reducts are not replaceable each other for the coming objects in the future. On the other hand, value reduction is to reduce the decision rules to a logically equivalent minimal subset of minimal length. Traditionally, the value reduct has been searched through the attribute reduct. This method may miss important decision rules. In this paper, a novel method is presented to ind associative decision rules in a decision table by value reduction only using the association rule mining technology. Value reduction is conducted in a bottom-up fashion to induce the decision rules without inding any attribute reducts. Our method is described and demonstrated with an illustrative example. Keywords- Associative decision rules, rough set theory, data reduction, atribute reducts, association rule mining I. INTRODUCTION Rough set theory has been developed as an elegant and powerul methodology in extracting and minimizing decision rules rom decision tables and has been extensively studied in the ield and applied in real-life applications [4-15]. The essence of rough set theory is to reduce a given decision table small enough such that decision rules can be directly extracted. The reduction in rough set theory can be summarized as three aspects: row (tuple) reduction, column (attribute) reduction, and cell (value) reduction. Row reduction is only merging duplicate rows, atribute reduction is to fmd important atributes, and value reduction simpliies decision rules. Most algorithms and approaches to inding 978-1-4673-2311-6/12/$31.00 ©2012 IEEE decision rules follow these three steps in order. Since there may exist various atribute reducs, many efforts have been put on seeking the best or optimal reduct in the sense of accurate decisions. However, different atribute reducts are only equivalent in the circumstance of the given decision table. The decision rules that are induced rom different atribute reducts are not replaceable each other for the new objects in the uture. On the other hand, value reduction is to reduce the decision rules to a logically equivalent minimal subset of minimal length. Traditionally, the value reduct has been searched through the atribute reduct, which may miss important decision rules, although some authors have presented the other way to fmd value reduct irst, and then atribute reducts. But very little effort has been made to ind value reducts directly to induce decision rules without fmding any atribute reducts. Unlike traditional rough set theory where decision rules are exracted rom atribute reducts, we present an approach to exracting a set of associative decision rules by fmding value reduct directly in a decision table without fmding any atribute reducts. Our method uses the itemset concept exploited in mining association rules [1], [2], [3]. A bottom up algorithm is proposed to generate itemsets which are actually sub-decision tables of the original one. The rest of this paper is organized as follows. In Section II, the raditional data reduction approach to finding decision rules in a decision table is illusrated with an example to distinguish atribute reduct and value reduct. The drawback of the traditional approach is analyzed and the related work is reviewed in Section III. Our bottom-up approach to finding value reduct without finding attribute reducts is presented and its implementation is considered in Section IV, Section V is the conclusion. II. TRADITIONAL DATA REDUCTION TO FIND DECISION RULES Attribute reduction is to fmd attribute reducts. The cenral notions in this research are core, reduct and knowledge dependency [5]. n atribute reduct of a decision table is a subset of condition atributes that suice to defme the decision atributes. More than one reduct for each decision table may exist. The intersection of all the possible reducts is called the core, which represents the most important information of the decision table. Finding all atribute reducts in a decision table is NP-hard [6] unfortunately, so the ull power of rough set methodology may only be effective on clean and small sets of data.