complex systems or situations (Huang, Tzeng, & Ong, 2005). The implementation of ISM is dependent on through individual or group mental feedback to calculate relation matrix to present the interdependences between the elements composing a management system.
Referring to Huang et al.’s (2005) study, the procedures of ISM are illustrated as follows:
The initial relation matrix is formed by asking the question like “Does the element influence the element ?” If the answer is “Yes”, then 1, otherwise 0. In other words, the initial relation matrix is equal to a binary matrix. Equation 1 presents the general form of the relation matrix:
0 0
0
(1)
where means the ith element in the system, denotes the direct impact of ith element on jth element. Thus, is the initial relation matrix.
After constructing the initial relation matrix, the reachability matrix, , need to be calculated by using Equation (2) and (3) as follows:
(2)
, 1 (3)
where is the unit matrix, and denotes the powers. Note that the reachability matrix is under the operators of the Boolean multiplication and addition, and is obtained by powering the matrix, , to satisfy the Equation (3).
Unfortunately, ISM based on using binary matrix just can be used for understand the
existence of the causal relationship between the elements, but not for the degree of the
impact of a certain element on the other ones. Thus, Decision-Making Trial and Evaluation
Laboratory method that can be used to present the impact of each element on others isintroduced in next section.
2. Decision-making trial and evaluation laboratory
Decision-Making Trial and Evaluation Laboratory (DEMATEL) was proposed by
Battelle Geneva Institute to demonstrate the causality between practices in a system by gathering collective knowledge. Referring to previous relevant literatures, the operational procedure of DEMATEL is summarized and introduced in the following steps:Step 1: Building the initial average direct-relation matrix
Suppose is the number of experts consulted, and is the number of practices that each expert considers. The integer score refers to the degree that practice i affects practice j for the kth expert, where the scores 0, 1, 2, 3, 4 represent the range from ‘no influence’ to ‘very high influence.’ The average matrix is realized by averaging all the experts’ scores and can be represented mathematically by the following equation:
1 (4)
Step 2: Calculating the normalized direct-relation matrix
The normalized direct-relation matrix is obtained by normalizing the direct-relation matrix and can be represented mathematically by the following equation:
, where ∑ , ∑ (5)
Since the sum of each row i of matrix represents the direct effects that practice i gives to the other practices, and the sum of each column j of matrix represents the direct effects that practice i receives from the other practices, therefore, ∑ ,
∑ represents the direct effects of the practice with the most direct given and received effects on others.
Step 3: Deriving the total relation matrix
The total relation effects include both the indirect effects and direct effects. Since there is a continuous decrease of the indirect effects of problems along the powers of matrix , the total relation matrix, , is defined as a matrix, and is the identity matrix. The mathematical equation can be represented as follows:
(6)
Step 4: Calculating the total effects and net effects to depict the Impact-Direct Map (IDM)
Define and as 1 vectors as the sum of rows and the sum of columns, respectively, of the total relation matrix . The mathematical equations can be represented as follows:(7)
(8)
The sum shows the total given effects, both directly and indirectly, that practice i has on the other practices. The sum shows the total received effects, both directly and indirectly, that all the other practices have on practice j. Thus, the sum gives us an index representing the total effects both given and received by practice i. In addition, the difference shows the net effects or the net contribution by practice i on the system. When is graphed on the x-axis and is graphed on the y-axis, the IDM can then be produced.
Step 5: Set a threshold value to obtain the Impact-Relations Map (IRM)
To explain the structural relation among practices while keeping the complexity of the
whole system to a manageable level, it is necessary to set a threshold value to filter out the negligible effects in matrix , that is only the practices whose effect in matrix is greater than the threshold value will be shown in the IRM. For example, there is a matrix as shown in Figure 10-(a). If a threshold value 0.25 is chosen, then the IRM can be presented as Figure 10-(b):
Figure 10 Example of IRM
The diagraph portrays a basic concept of contextual relation among the criteria of the system, in which the numeral represents the strength of influence (Yang & Tzeng, 2011).
Thus, the DEMATEL method is widely used in recent year to build the structure of relationship map for clarifying theinterrelations of criteria and to visualize the complicate causal relationships between criteria in a real system, and has been successfully applied to various management circumstances. Based on the Carnevalli and Miguel’s (2008) meta-analysis scheme (referred to Appendix A), more details about the recent DEMATEL-based literatures are summarized in Table 6.
T =
0.17 0.18 0.16 0.28 0.26 0.17 0.25 0.32 0.22 0.23 0.13 0.28 0.32 0.26 0.22 0.25 A
B C D
A B C D
Threshold value (m = 0.25)
A
B C
D
(a) Example of TRM (b) Example of IRM
Table 6
Summary of DEMATEL-based literatures
Author (year) Kind of study (T1) DEMATEL application (T9) DEMATEL advanced methodology
Yang and Tzeng (2011) A, F: 3C component manufacturer
A6, A7: for the selection of competent vendors
Adopting the influence level values from DEMATEL as the base of normalization super-matrix for calculating ANP weights to obtain the relative importance.
Jassbi, Mohamadnejad, and Nasrollahzadeh
(2011)
F: Trading Company A1, A6: for building strategy map as the basis of its Balanced Scorecard
To deal with the ambiguity of human assessments, the extended fuzzy DEMATEL is proposed.
Lin, Yang, Kang, and Yu (2011)
F: Semiconductor industry
A1, A6: to explore the core competences and causal effect of the
IC design service company
none
Wu (2008) F: Semiconductor industry
A1: to evaluate and select knowledge management (KM) strategies
The ANP model is used to calculate the weights of elements of clusters, and the DEMATEL is used to deal with the situation when inner dependences occur within an evaluation cluster. Then, the optimal solution can be selected according to the overall priorities of the alternatives.
Lin and Tzeng (2009) F: Science/technology park
A1: to build the value-created system of science/technology park to advance
the parks’ value
none
Lee et al. (2010) F: plasma etching manufacturing industry
A1, A2: to evaluate users’ behavioral intention toward using new technology
Using DEMATEL to re-analyze and explain the interaction relationship and impact level between variables of technology acceptance model (TAM2).
Table 6 (con.)
Author (year) Kind of study (T1) DEMATEL application (T9) DEMATEL advanced methodology
Büyüközkan and
Öztürkcan (2010) F: Logistics company A7: to help companies determine critical Six Sigma projects
First of all the Six Sigma project evaluation dimension and components are determined. DEMATEL approach is then applied to construct interrelations among criteria. The weights of criteria are finally obtained through ANP.
Seyed-Hosseini, Safaei, and Asgharpour (2006)
F: turbocharger manufacturer
A1, A2: to reprioritize failure modes for corrective actions
The DEMATEL method is applied for understand the interdependence between potential failure modes and causes of failure in a Failure Mode and Effects Analysis (FMEA), and then the RPN are regarded as an input data for DEMATEL method.
Lin and Wu (2008) F: high-tech company A7: to develop a structural model for evaluating and selecting R&D projects
A fuzzy DEMATEL method for group decision-making is proposed to gather group ideas and analyze the cause-effect relationship of complex problems in fuzzy environments.
Tseng (2009) F: estate agent sector A7: to develop a service quality model with uncertainty to rank the best agent
A degree of grey possibility is used to determine the ranking order of all alternatives expressed in fuzzy numbers. Then, the DEMATEL method can convert the relationship between the causes and effects of criteria into a structural system.
Note: The symbol [ ] represent the integration with analytic network process (ANP); the symbol [ ] represent the integration with Grey; the symbol [ ] represent the integration with Fuzzy; the symbol “ ” represent the integration with other methodologies.