Supplier selection in a fuzzy group setting is a very important strategic decision involving decisions balancing a number of conflicting criteria and opinions from different experts. This paper uses grey related analysis and Dempster–Shafer theory to deal with this fuzzy group decision making problem. First, in the individual aggregation, grey related analysis is employed as a means to reflect uncertainty in multi-attribute models through interval numbers. Second, in the group aggregation, the Dempster–Shafer (D–S) rule of combination is used to aggregate individual preferences into a collective preference, by which the candidate alternatives are ranked and the best alternative(s) are obtained. The proposed approach uses both quantitative and qualitative data for international supplier selection. It provides alternative tools to evaluate and improve supplier selection decisions in an uncertain global market.
Supplier selection involves the need to trade-off multiple criteria, as well as the presence of both quantitative and qualitative data. With the increase in outsourcing, offshore sourcing, and various electronic businesses, these decisions are becoming ever more complex. When more experts (and more conflicting opinions) are involved, this decision becomes a problem of selecting ideal suppliers in a fuzzy group setting.
Various studies have presented methods to aggregate different expert opinions in a fuzzy group decision making problem (Kulak and Kahraman, 2005 and Zhang et al., 2005). One of the key issues is how to choose the aggregation operators and functions to combine different degrees of membership into one numerical value. Expert opinions, a common way to hedge risk, can be represented by fuzzy numbers when subjectivity, vagueness and imprecision enter into those assessments (Bardossy, Duckstein, & Bogardi, 1993). A number of studies have used fuzzy preference relations (Fedrizzi et al., 1980, Kacprzyk and Fedrizzi, 1988, Kacprzyk et al., 1992, Nurmi, 1981, Tanino, 1984 and Tanino, 1990), and Ishikawa et al. (1993) used an interval value to represent judgments of experts and derived a group consensus judgment from cumulative frequency distribution. Recently, Hsu and Chen (1996) proposed a method called similarity aggregation to aggregate individual opinions of experts. To date, more than ninety families of operators have been extensively studied ( Beliakov & Warren, 2001).
Of these, TOPSIS (order preference by similarity to ideal solution) (Hwang & Yoon, 1981) and LINMAP (linear programming for multidimensional analysis of preference) (Srinivasan & Shocker, 1973) are the two functions most relevant to this paper. TOPSIS computes both a positive ideal solution (PIS) and a negative ideal solution (NIS) from the decision matrix and then generates the best compromise alternative with the shortest distance to PIS and the farthest from NIS. The LINMAP method uses pair-wise comparisons of alternatives given by decision makers and generates the best compromise alternative as the solution that has the shortest distance to the positive ideal solution. Both TOPSIS and LINMAP try to generate the best compromise alternative as the solution nearest to the PIS, as does Deng’s grey related analysis (Deng, 1982). Grey system theory addresses the concept that information is sometimes incomplete or unknown. The intent is the same as in factor analysis, cluster analysis, and discriminant analysis, except that those methods often do not work well when sample size is small and sample distribution is unknown. Interval numbers are standardized through norms, which allow transformation of index values through product operations (Zhang et al., 2005). Grey system theory provides another tool to reflect uncertainty into the multi-attribute model, using reference number sequence rather than the ideal solution of TOPSIS and LINMAP.
This paper proposes a hybrid method using Deng’s grey system theory and Dempster–Shafer evidence theory (Dempster, 1966, Dempster, 1967, Dempster, 1968 and Shafer, 1976). The proposed grey-evidence hybrid solves fuzzy group decision-making problems in two phases: First, grey related analysis is used to reflect uncertainty between experts in multi-attribute models through interval numbers, generating individual preferences. Second, the Dempster–Shafer (D–S) rule of combination is used to aggregate individual preferences into collective preferences by which the best alternative(s) are obtained.
Compared to probability theory, D–S evidence theory captures more information to support decision-making, by identifying the uncertain and unknown evidence. It provides a mechanism to derive solutions from various vague evidences without knowing much prior information. Combining both theories enables the ultimate decision makers to take advantage of both methods merits and use experts to deal with uncertainty and risk confidently.
Using the proposed approach, we solved a complex international supplier selection problem in the fuzzy group setting, taking both quantitative and qualitative data into consideration. The results show that the proposed approach simplifies and speeds up trade-off analysis among costs, quality acceptance levels, on-time delivery, and risk factors, and opens up the possibility of a family of tools to evaluate and improve other selection decisions in an uncertain global market.
The rest of the paper is organized as follows: we start with reviewing the Dempster–Shafer theory of combination in Section 2. Section 3 delivers the method and Section 4 demonstrates the application of the proposed method to international supplier selection problem. Section 5 concludes the paper.
