A new group-based screening approach with visual presentation
Introduction
Screening, ranking and selecting are the three main stages in the process of finding user preferences in multi-criteria decision-making (MCDM) problems (Brugha, 2004). Screening is a process of filtering out items that are less likely to be selected (Hobbs & Meier, 2000); thereby, the item set can be compressed into a smaller item set, making it easier for decision makers to focus on evaluating items in the smaller set.
One of the main difficulties in solving MCDM problems is determining the decision maker’s preferences by discovering the weight of each criterion. Chen et al. (2008) developed a well-known case-based distance screening method to find the decision maker’s preferences by selecting acceptable and unacceptable cases. The case-based distance screening method does not directly ask decision makers for the weights of criteria, but instead derives preferential information based on the acceptable and unacceptable cases in the test set selected by decision makers. A given target point serves as a reference point. From the selected test set, the weights of criteria and a distance threshold that separates acceptable and unacceptable cases are obtained. Alternatives whose distance to the target point is greater than the distance threshold can be screened out. The case-based distance screening method is simple to understand and easy to implement because decision makers do not have to directly identify tradeoff weights or dominance relationships, nor do they have to assume utility functions; however, as the objective of the case-based distance screening model is to minimize the overall squared error, the number of misclassifications may be large.
In addition, graphic presentation can help a decision maker to better observe the decision context (Meyer, 1991, Ma and Li, 2011). Keeney (2002) pointed out that misunderstanding the decision context is a key mistake (among 12) that people frequently make when making decisions. In order to improve the misclassification rate and provide visual aids, Ma (2012) proposed an extended case-based distance approach to help decision makers screen alternatives visually, by incorporating the concept of the mixed-integer programming approach of discriminant analysis (MIP-DA) (Sueyoshi, 2004, Sueyoshi and Hwang, 2004) and the multidimensional scaling (MDS) technique (Cox & Cox, 2000). The MIP-DA method estimates the weight of items by minimizing the total number of misclassifications instead of the total squared error, thereby reducing the misclassification rate. While Ma’s study (2012) minimizes the number of misclassifications rather than the overall squared error, it has the following limitations: (i) minimizing the misclassification rate may lead to a considerably increased overall squared error. (ii) The efficiencies of individual screening may be insufficient, especially when there are a large number of alternatives.
The present study proposes a new visual group-based screening approach to improve the above-mentioned limitations. First, this study constructs two revised models (Models 1 and 2) to improve previous screening and displaying models. The concept of similarity upper approximation (Kumar et al., 2006, Mishra et al., 2015) is then employed to provide group-based screening solutions. Lastly, a new visualization model (Model 3) is proposed to simultaneously allocate, group and screen alternatives.
Compared to previous methods, the proposed approach can provide flexibility, enabling decision makers to adopt a group-based or individual-based screening method. In addition, the group of alternatives, relationships among alternatives and cases, and the acceptable ring can be visualized directly, thereby assisting a decision maker in observing the decision context and making a better decision.
Section snippets
Related works
In multi-criterion decision problems, acquiring the decision maker’s preference in the form of item weights is usually a difficult process. Based on different kinds of preference information specified by decision makers, Chen et al. (2008) categorized four types of screening methods: tradeoff weights, non-tradeoff weights, data envelopment analysis (DEA) (Charnes et al., 1961, Partovi, 2011), and aspiration-level methods.
Tradeoff weight-based screening methods adopt an additive weighting model
The proposed approach
This study aims to develop a new visual group-based screening approach. First, revised models for improving previous screening and display models are developed. A visual model for simultaneously allocating, screening and grouping alternatives is then constructed.
While the case-based distance model (Chen et al., 2008) minimizes the overall squared errors, the number of misclassifications may be large. Conversely, while the extended case-based distance model (Ma, 2012) minimizes the number of
A numerical example
In order to make comparisons, the office-renting example (Ma, 2012), originally modified from the Harvard Business Review (Hammond et al., 1998), is applied here (denoted as Example 1) to demonstrate the proposed approach. A decision maker sets five criteria for finding an office to rent: short commute time, convenient access, good service, adequate space and low cost. The original data, lower and upper bound, and the best target value are shown in Table 1.
In this example, the decision maker
Comparisons and discussion
Four approaches: the CBD method (Chen et al., 2008), the MIP-DA method (Sueyoshi, 2004), the ECBD method (Ma, 2012), and the proposed approach herein are compared and discussed. For Example 1, the results of four different approaches are listed in Table 7.
The numbers of misclassified cases for these four methods are 4, 1, 1, and 1 with misclassification rate 57%, 14%, 14%, and 14%, respectively. The squared error of case classification is 0.000, 0.079, 0.146, and 0.016, respectively. As we can
Conclusions
This study develops a new visual group-based screening approach. Revised models to improve previous screening and displaying models are constructed herein. The concept of the similarity upper approximation is employed to provide group-based screening solutions. Lastly, a new visualization model is introduced to simultaneously allocate, group and screen alternatives.
Compared to previous methods, the proposed approach has the lowest misclassification rate, while simultaneously yielding the
CRediT authorship contribution statement
Li-Ching Ma: Conceptualization, Methodology, Software, Validation, Formal analysis, Visualization, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported by the Ministry of Science and Technology of the Republic of China [grant number: MOST 108-2410-H-239-011-MY3].
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