Chapter 3 Research Methodology
3.3. The DEMATEL Method
Decision Making Trial and Evaluation Laboratory (DEMATEL) method was originally developed by the Science and Human Affairs Program of the Battelle Memorial Institute of Geneva in 1970s, with the purpose of studying the complex ‘real world problems’ dealing mainly with interactive man-model techniques and evaluating qualitative and factor-linked aspects of societal problems (Gabus & Fontela, 1972).
DEMATEL technique was developed with the belief that the pioneering and proper use of scientific research methods could help to illuminate specific and intertwined phenomena and contribute to the recognition of practical solutions through a hierarchical structure. The applicability of the method is widespread, ranging from industrial planning and decision-making to urban planning and design, regional environmental assessment, analysis of world problems, and so forth. It has also been successfully applied in many situations, such as marketing strategies, control systems, safety problems, developing the competencies of global managers and group decision-making. Furthermore, a hybrid model combining the two methods has been widely used in various fields, for example, e-learning evaluation (Tzeng, Chiang & Li, 2007), airline safety measurement, and intelligent global manufacturing & logistics systems (Tzeng & Huang, 2007). Therefore, in this paper we use DEMATEL not only to detect complex relationships and build a Network Relation Map (NRM) of the criteria, but also to obtain the influence levels of each element over others. The
DEMATEL method is based upon graph theory, enabling us to plan and solve problems visually, so that we may divide multiple criteria into a relationship of cause and effect group, in order to better understand causal relationships. Directed graphs (also called digraphs) are more useful than directionless graphs, because digraphs will demonstrate the directed relationships of sub-systems. This method is used to analyze and form the relationship of cause and effect among evaluation criteria or to derive interrelationship among factors. It has been widely accepted as one of the best tools to solve the cause and effect relationship among the evaluation criteria (Huang et al., 2007; Chiu et al., 2006).
Therefore, in this study we use DEMATEL not only to detect complex relationships and build a NRM of the criteria, but also to obtain the influence levels of each element over others; we then adopt these influence level values as the basis of the normalization supermatrix for determining ANP weights to obtain the relative importance. To apply the DEMATEL method smoothly, the authors refined the definitions based on above authors, and produced the essential definitions indicated below. The DEMATEL method is based upon graph theory, enabling us to plan and solve problems visually, so that we may divide multiple criteria into a relationship of cause and effect group, in order to better understand causal relationships. Directed graphs (also called digraphs) are more useful than directionless graphs, because digraphs will demonstrate the directed relationships of sub-systems. A digraph typically represents a communication network, or a domination relationship between individuals, etc. Suppose a system contains a set of elements, S = {s1, s2, . . . , sn}, and particular pair-wise relationships are determined for modeling, with respect to a mathematical relationship, MR. Next, portray the relationship MR as a direct-relation matrix that is indexed equally in both dimensions by elements from the set S. Then,
extract the case for which the number 0 appears in the cell (i, j ), if the entry is a positive integral that has the meaning of: the ordered pair (si, sj ) is in the relationship MR; it has the kind of relationship regarding that element such that si causes element sj . The digraph portrays a contextual relationship between the elements of the system, in which a numeral represents the strength of influence (Fig. 4). The elements s1, s2, s3 and s4 represent the factors that have relationships in Fig. 2. The number between factors is influence or influenced degree. For example, an arrow from s1 to s2 represents the fact that s1 influences s2 and its influenced degree is two. The DEMATEL method can convert the relationship between the causes and effects of criteria into an intelligible structural model of the system (Chiu et al., 2006).
Figure 3: An Example of the Directed Graph.
Source: Huang et al., 2011.
Definition 1 The pair-wise comparison scale may be designated as m levels, where the scores 0, 1, 2, . . . , m represent the range from ‘no influence’ to ‘very high influence’.
Definition 2 The initial direct relation/influence matrix A is an n × n matrix obtained
by pair-wise comparisons, in terms of influences and directions between the
Definition 3 The normalized direct relation/influence matrix N can be obtained through (1) and (2), in which all principal diagonal elements are equal to zero.
zA
Definition 4 Then, the total relationship matrix T can be obtained using (3), where I stands for the identity matrix. T NN2N N(IN)1, (3) where
The (i, j ) element tij of matrix T denotes the direct and indirect influences of factor i on factor j .
Definition 5 The row and column sums are separately denoted as r and c within the total-relation matrix T through (4), (5), and (6).
T NN2N (4)
where the r and c vectors denote the sums of the rows and columns, respectively.
Definition 6 Suppose ri denotes the row sum of the ith row of matrix T . Then, ri is the sum of the influences dispatching from factor i to the other factors, both directly and indirectly. Suppose that cj denotes the column sum of the jth column of matrix T. Then, cj is the sum of the influences that factor i is receiving from the other factors.
Furthermore, when i = j (i.e., the sum of the row sum and the column sum (ri + ci ) represents the index representing the strength of the influence, both dispatching and receiving), (ri + ci ) is the degree of the central role that factor i plays in the problem. If (ri −ci ) is positive, then factor i primarily is dispatching influence upon the strength of other factors; and if (ri − ci ) is negative, then factor i primarily is receiving influence from other factors (Huang et al., 2007; Liou et al., 2007; Tamura et al., 2002).