In a recent paper by Toloo et al. [Toloo, M., Sohrabi, B., & Nalchigar, S. (2009). A new method for ranking discovered rules from data mining by DEA. Expert Systems with Applications, 36, 8503–8508], they proposed a new integrated data envelopment analysis model to find most efficient association rule in data mining. Then, utilizing this model, an algorithm is developed for ranking association rules by considering multiple criteria. In this paper, we show that their model only selects one efficient association rule by chance and is totally depended on the solution method or software is used for solving the problem. In addition, it is shown that their proposed algorithm can only rank efficient rules randomly and will fail to rank inefficient DMUs. We also refer to some other drawbacks in that paper and propose another approach to set up a full ranking of the association rules. A numerical example illustrates some contents of the paper
In multiple criteria decision making, each alternative is evaluated based on a number of different criteria. One popular solution method for a multiple criteria problem is to obtain weights for criteria and use the weighted sum of the criteria as the score for each alternative. These scores can be utilized for ranking the alternatives or selecting one with the biggest score as the final decision. The important question here is how to obtain these weights. There are many methods for this purpose; one of them is data envelopment analysis (DEA), a linear programming based method introduced by Charnes, Cooper, and Rhodes (1978). DEA uses the best favorable weights corresponding to each decision making unit (DMU) to obtain the scores.
In a recent paper, Chen (2007) used DEA in a data mining problem, to evaluate association rules with multiple criteria. For this purpose, Chen used the approach of Obata and Ishii (2003), which has been proposed for voting system. In Obata and Ishii approach, the proposed DEA/AR model of Cook and Kress (1990) is utilized first, to obtain efficiency scores, and then another model is used to discriminate efficient candidates. The candidates in data mining are the association rules (DMUs in DEA and alternatives in multiple criteria decision making), which are evaluated based on some criteria.
In a more recent paper, Toloo, Sohrabi, and Nalchigar (2009) proposed another DEA approach for data mining. They counted some advantages of their method; one of the advantages was providing a full ranking for the association rules, which we will show to be not correct. We will refer to some disadvantages of their method and it will be shown that their proposed algorithm can only rank efficient DMUs randomly. In addition it will be shown that the model is used in their algorithm will be infeasible corresponding to inefficient DMUs. In general, their model is not convenient to rank efficient DMUs, and will fail to rank inefficient DMUs.
As a convenient full ranking approach for this problem, we suggest a slightly modified method of Foroughi and Tamiz (2005). In addition, to improve the approach and decrease the number of models and constraints, we have developed an algorithm, by modifying and simplifying the proposed algorithm of Toloo et al., to obtain efficient DMUs. The algorithm will improve the model particularly when we need only to rank efficient DMUs or select one association rule. It will be seen that the proposed approach will provide a full ranking of the rules for the example of market basket analysis, which was used by Chen, 2007 and Toloo et al., 2009.
In this paper, we first referred to some drawbacks and errors in a recent paper by Toloo et al. (2009). We showed that their proposed model for obtaining most efficient DMU can only select one DMU from efficient DMUs by chance. As a result, their algorithm can only rank the efficient DMUs randomly. In addition, they claimed their algorithm can rank all DMUs, and they referred this as an advantage for their model in comparing with the used approach by Chen (2007). We showed also that this is not correct and the used model in their algorithm will be infeasible after ranking the efficient DMUs randomly, and so will fail to rank inefficient DMUs. To overcome these problems, we proposed another approach which is similar to the method of Foroughi and Tamiz (2005) in voting system. We also revised the algorithm of Toloo et al. (2009) to obtain efficient DMUs and improve the proposed approach. The numerical example shows that the proposed approach can rank all the association rules in Chen’s example for data mining.
