Please cite this article in press as: C.-H. Chen, et al., A fuzzy coherent rule mining algorithm, Appl. Soft Comput. J. (2013), http://dx.doi.org/10.1016/j.asoc.2012.12.031 ARTICLE IN PRESS G Model ASOC-1863; No. of Pages 7 Applied Soft Computing xxx (2013) xxx–xxx Contents lists available at SciVerse ScienceDirect Applied Soft Computing j ourna l h o mepage: www.elsevier.com/locate/asoc A fuzzy coherent rule mining algorithm  Chun-Hao Chen a,∗ , Ai-Fang Li a , Yeong-Chyi Lee b a Department of Computer Science and Information Engineering, Tamkang University, Tamsui, New Taipei 25137, Taiwan, ROC b Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan, ROC a r t i c l e i n f o Article history: Received 6 June 2012 Received in revised form 13 September 2012 Accepted 30 December 2012 Available online xxx Keywords: Fuzzy set Fuzzy association rules Fuzzy coherent rules Membership function Data mining a b s t r a c t In real-world applications, transactions usually consist of quantitative values. Many fuzzy data mining approaches have thus been proposed for finding fuzzy association rules with the predefined minimum support from the give quantitative transactions. However, the common problems of those approaches are that an appropriate minimum support is hard to set, and the derived rules usually expose common-sense knowledge which may not be interesting in business point of view. In this paper, an algorithm for mining fuzzy coherent rules is proposed for overcoming those problems with the properties of propositional logic. It first transforms quantitative transactions into fuzzy sets. Then, those generated fuzzy sets are collected to generate candidate fuzzy coherent rules. Finally, contingency tables are calculated and used for checking those candidate fuzzy coherent rules satisfy the four criteria or not. If yes, it is a fuzzy coherent rule. Experiments on the foodmart dataset are also made to show the effectiveness of the proposed algorithm. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Data mining is most commonly used in attempts to derive use- ful information and extract useful patterns from large data sets or database for solving specific issue. One of the commonly used techniques is association rule mining which is an expression X → Y, where X and Y are a set of items [2]. It means in the set of transac- tions, if all the items in X exist in a transaction, then Y is also in the transaction with a high probability. For example, assume when- ever customers in a supermarket buy bread and butter, they will also buy milk. From the transactions kept in the supermarkets, an association rule such as “Bread and Butter → Milk” will be mined out. Lots of mining approaches are thus proposed for associ- ation rule mining [1,2,4,11], and most of them focused on binary valued transaction data. However, transaction data in real- world applications usually consist of quantitative values. Thus, by combing fuzzy theory, many mining algorithms have been proposed for deriving fuzzy rules from quantitative transaction database [3,5,13,14,16–19,25,26,29–31,37,39]. Some mining algo- rithms have also been applied on control problem and classification [4,21]. In [4], Kianmehr et al. adopt a multi-objective genetic algo-  This is a modified and expanded version of the paper “Mining Fuzzy Coher- ent Rules from Quantitative Transactions without Minimum Support Threshold,” accepted and to appear in International Conference on Fuzzy Systems, 2012. ∗ Corresponding author. E-mail addresses: chchen@mail.tku.edu.tw (C.-H. Chen), 697410172@s97.tku.edu.tw (A.-F. Li), yeongchyi@csu.edu.tw (Y.-C. Lee). rithm based clustering method for determining and optimizing the membership functions of the fuzzy sets. In [21], Alcalà-Fdez et al. present a new fuzzy association rules classification method for high-dimensional problems. However, there are two common problems of those fuzzy asso- ciation rule mining approaches. The first one is that how to set appropriate minimum support and minimum confidence in fuzzy data mining. Obviously, it is a difficult task. If a large minimum support value is set, lots of potential rules may be deleted. On the contrary, large amount of rules will be derived such that decision makers cannot use them easily to make right decisions. The second problem is that some of those derived rules only expose common- sense knowledge and may not be interesting in business point of view. For example, if a rule “If milk is bought, Then bread is bought,” is derived with high support and confidence, it is a reliable rule according to Apriori algorithm [1]. But, it may not be valuable for business since the derived rule is common-sense knowledge, and it may mislead users because the rule “If milk is bought, Then bread is not bought” may also exist simultaneously. Recently, Longbing Cao suggested the domain-driven data mining concept (D 3 M) [7,9,10], and cooperated it with industry knowledge to mine actual and useful information. Under the D 3 M concept, for those association rule mining algorithms on binary transaction [33], Sim et al. proposed a logical-based approach for deriving coherent rules. In that approach, by using the properties of propositional logic, relationship between items (also namely coher- ent rules) can be directly derived without knowing the appropriate value of minimum support. 1568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2012.12.031