A multi-level ant-colony mining algorithm for membership functions Tzung-Pei Hong a,b,⇑ , Ya-Fang Tung c , Shyue-Liang Wang d , Yu-Lung Wu c , Min-Thai Wu b a Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung 811, Taiwan b Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan c Institute of Information Management, I-Shou University, Kaohsiung 840, Taiwan d Department of Information Management, National University of Kaohsiung, Kaohsiung 811, Taiwan article info Article history: Available online 11 January 2011 Keywords: Data mining Ant system Ant colony system Fuzzy set Membership function Multi-stage graph abstract Fuzzy data mining is used to extract fuzzy knowledge from linguistic or quantitative data. It is an extension of traditional data mining and the derived knowledge is relatively mean- ingful to human beings. In the past, we proposed a mining algorithm to find suitable mem- bership functions for fuzzy association rules based on ant colony systems. In that approach, precision was limited by the use of binary bits to encode the membership functions. This paper elaborates on the original approach to increase the accuracy of results by adding multi-level processing. A multi-level ant colony framework is thus designed and an algo- rithm based on the structure is proposed to achieve the purpose. The proposed approach first transforms the fuzzy mining problem into a multi-stage graph, with each route repre- senting a possible set of membership functions. The new approach then extends the previ- ous one, using multi-level processing to solve the problem in which the maximum quantities of item values in the transactions may be large. The membership functions derived in a given level will be refined in the subsequent level. The final membership func- tions in the last level are then outputted to the rule-mining phase to find fuzzy association rules. Experiments are also performed to show the performance of the proposed approach. The experimental results show that the proposed multi-level ant colony systems mining approach can obtain improved results. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction Knowledge Discovery and Data Mining (KDD) refers to the application of nontrivial procedures for identifying effective, coherent, potentially useful, and previously unknown patterns in large databases [11]. The fast growth of KDD has spurred the development of many related techniques and applications based on different approaches including classification rules, clustering, association rules, and others. Since 1993, the practice of inducing association rules from transaction data has been commonly used in KDD [1]. An association rule is an expression X ? Y, where X is a set of items and Y is usually a single item. In the set of transactions, if all the items in X exist in a transaction, then there is a high probability of Y also being in the transaction. For example, assuming that transactions including the purchase of bread are usually accompanied by the pur- chase of milk, then the association rule ‘‘bread ? milk’’ will be induced. Most previous studies focused on binary valued transaction data. Transaction data in real-world applications, however, usually consist of quantitative values. Hong et al. [13] thus proposed a mining approach that integrated fuzzy-set concepts with the apriori mining algorithm to find interesting fuzzy itemsets and association rules in quantitative transaction data. In 0020-0255/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2010.12.019 ⇑ Corresponding author at: Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung 811, Taiwan. E-mail addresses: tphong@nuk.edu.tw, tphong@ksmail.seed.net.tw (T.-P. Hong), m9522030@stmail.isu.edu.tw (Y.-F. Tung), slwang@nuk.edu.tw (S.-L. Wang), wuyulung@isu.edu.tw (Y.-L. Wu), d953040015@student.nsysu.edu.tw (M.-T. Wu). Information Sciences 182 (2012) 3–14 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins