Integration of semi-fuzzy SVDD and CC-Rule method for supplier selection

Abstract

A model based on semi-fuzzy support vector domain description (semi-fuzzy SVDD) is put forward to address multi-classification problem involved in supplier selection. By preprocessing using semi-fuzzy kernel clustering algorithm, original samples are divided into two subsets: deterministic samples and fuzzy samples. Only the fuzzy samples, rather than all original ones, require expert judgment to decide their categories and are selected as training samples to accomplish SVDD specification. Therefore, the samples preprocessing method can not only decrease experts working strength, but also achieve less computational consumption and better performance of the classifier. Nevertheless, in order to accomplish practical decision making, another condition has to be met: good explanations to the decision. A rule extraction method based on cooperative coevolution algorithm (CCEA), is introduced to achieve the target. To validate the proposed methodology, samples from real world were employed for experiments, with results compared with conventional multi-classification support vector machine approaches and other artificial intelligence techniques. Moreover, in terms of rule extraction, experiments on key parameters, different methods including decompositional and pedagogical ones etc. were also conducted.

Introduction

Supplier selection is a complex multi-criteria decision making problem, on which some conflicting criteria might be considered and evaluated. Decisions are complicated due to many dynamic factors, such as uncertain price, capacity, and demand etc. So, issues in supplier selection have received extensive attentions, with some valuable academic surveys accomplished (Ho et al., 2010, Jain et al., 2009). Moreover, a systemic literature review on the latest development in this area was presented in Chai, Liu, and Ngai (2013). Among the proposed methodologies and techniques, support vector machine, one of promising machine learning methods, has begun to play more important roles, which can be seen in section 1. However, in terms of supplier selection using the method, some problems still exist, which can be concluded as follows:

Firstly, multi-classification problem should be addressed. That is, suppliers will usually be divided into more than two categories, while standard support vector machine based on hyper-plane cannot handle it directly.

Secondly, according to conventional methodologies, based on machine learning techniques, experts will be required to evaluate all training samples to determine their classification labels. Given complexity of the multi-classification problem, it is tiring and time-consuming to consider every training sample to decide its category. So, if only the ones, which are difficult to categorize and vital for classifier establishment, can be selected for expert judgment, working strength, possibility of human error and computational consumption can be reduced greatly.

Thirdly, in terms of supplier selection, good prediction accuracy alone cannot be considered as truly reliable decision support. Some supplementary information on how a verdict has been reached is also necessary. So, the method for rule extraction, which can discover attribute values connected to each possible outcome, is required. Although the models based on machine learning techniques can achieve high accuracies, the comprehensibility is limited. And it is a major drawback, which will cause reluctance to use the method.

Moreover, at the methodological level, rule extraction from support vector machine models, rather than from data directly, is also an important research issue (Barakat & Bradley, 2010). Methods based on standard support vector machine do not provide explanations or comprehensible justifications for the knowledge they learn. This has been shown to be one of the main obstacles impeding their practical applications. Hence, models based on support vector machine were integrated with some other approaches to accomplish rule extraction in different areas (He et al., 2006, Barakat, 2007, Castro et al., 2007, Martens et al., 2009, Ren et al., 2011, Zhu and Hu, 2013).

In terms of the problems mentioned above, motivations of the research can be concluded as follows:

• Develop a model suitable for handling multi-classification problem in supplier selection.

• Propose sample preprocessing method to ensure only the samples, which are difficult to categorize and vital for classifier establishment, are selected for expert judgment. Moreover, sample preprocessing is also expected to reduce the size of training set to decrease computational consumption and achieve better performance of the classifier.

• Develop techniques for rule extraction from multi-classification model, where the extracted rules are required to provide explanations to the classification results.

Therefore, a two-step hybridized method is proposed in the paper. In the first step, multi-classification classifier is developed with the thoughts of support vector domain description (SVDD) employed. Especially, training samples, selected from original ones after preprocessing, are deduced with their classification labels assigned using expert judgment. In the second step, CC-Rule method based on cooperative coevolution algorithm is introduced to achieve comprehensible rules extraction based on the set of support vectors obtained in the first step.