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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 3696457, 33 pages
https://doi.org/10.1155/2018/3696457
Review Article

DEMATEL Technique: A Systematic Review of the State-of-the-Art Literature on Methodologies and Applications

1School of Economics and Management, Tongji University, Shanghai 200092, China
2Institute for Manufacturing, University of Cambridge, Cambridge CB3 0FS, UK
3School of Management, Shanghai University, Shanghai 200444, China

Correspondence should be addressed to Hu-Chen Liu

Received 8 October 2017; Accepted 14 December 2017; Published 14 January 2018

Academic Editor: Marco Pizzarelli

Copyright © 2018 Sheng-Li Si et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Decision making trial and evaluation laboratory (DEMATEL) is considered as an effective method for the identification of cause-effect chain components of a complex system. It deals with evaluating interdependent relationships among factors and finding the critical ones through a visual structural model. Over the recent decade, a large number of studies have been done on the application of DEMATEL and many different variants have been put forward in the literature. The objective of this study is to review systematically the methodologies and applications of the DEMATEL technique. We reviewed a total of 346 papers published from 2006 to 2016 in the international journals. According to the approaches used, these publications are grouped into five categories: classical DEMATEL, fuzzy DEMATEL, grey DEMATEL, analytical network process- (ANP-) DEMATEL, and other DEMATEL. All papers with respect to each category are summarized and analyzed, pointing out their implementing procedures, real applications, and crucial findings. This systematic and comprehensive review holds valuable insights for researchers and practitioners into using the DEMATEL in terms of indicating current research trends and potential directions for further research.

1. Introduction

Decision making trial and evaluation laboratory (DEMATEL) technique was first developed by the Geneva Research Centre of the Battelle Memorial Institute to visualize the structure of complicated causal relationships through matrixes or digraphs [1]. As a kind of structural modeling approach, it is especially useful in analyzing the cause and effect relationships among components of a system. The DEMATEL can confirm interdependence among factors and aid in the development of a map to reflect relative relationships within them and can be used for investigating and solving complicated and intertwined problems. This method not only converts the interdependency relationships into a cause and effect group via matrixes but also finds the critical factors of a complex structure system with the help of an impact relation diagram.

Due to its advantages and capabilities, the approach of DEMATEL has received a great deal of attention in the past decade and many researchers have applied it for solving complicated system problems in various areas. In addition, the DEMATEL has been extended for better decision making under different environments since many real-world systems include imprecise and uncertain information. However, to the best of our knowledge, no systematic review has been performed for the DEMATEL technique and its applications. Therefore, in this study, we present a comprehensive review of the state-of-the-art literature regarding the approaches to decision making based on the DEMATEL. As a result of search using the Scopus database and following a methodological decision analysis, a total of 346 papers published in scientific journals from 2006 to 2016 were reviewed in detail. Based on the selected articles, the main objectives of this review are as follows: to summarize the DEMATEL methods that have been used in the academic literature, to reveal the different usage and application areas of these approaches, to show the current research trends in this field of study, and to find out the potential research directions in the future.

The remaining part of this paper is structured as follows: In Section 2, we introduce the research methodology used to identify and refine the literature in this study. In Section 3, detailed reviews of each category of the DEMATEL studies are presented. Section 4 describes some general observations and findings based on statistical analysis results of the review. Finally, this paper concludes in Section 5 by summarizing the results and discussing opportunities for future research.

2. Research Methodology

For the purpose of this literature review, we searched for articles in the Scopus database published between 2006 and 2016. The choice of this time period is based on the fact that the majority of papers on this topic were published during this period and there are only five articles recorded in the Scopus prior to 2006. Inspired by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISRMA) method [2, 3], the selection of articles in this study is consisted of three stages, that is, literature search, articles eligibility, and data extraction and summarizing. First, the keyword “DEMATEL” was used for searching in “abstract, title, and keywords” for journal papers, and a total of 509 document results were identified from Scopus. Next, we chose the articles which had used the DEMATEL technique or its extensions to solve real-world problems, and 346 academic papers fell under the scope of this review after title, abstract, and full-text screening. Since this study focuses on both the DEMATEL and its applications, those studies which only modify the DEMATEL technique without applying to actual settings have been eliminated (for the interested readers, please refer, e.g., to [46]). Finally, the resulting papers were reviewed thoroughly to identify the focus, method, application, and combination with other methods. Also articles were summarized based on various criteria such as year of publication, application areas, and citations.

Based on the DEMATEL methods adopted, the selected publications are roughly grouped into five categories: the ones using classical DEMATEL (105 articles), the ones using fuzzy DEMATEL (63 articles), the ones using grey DEMATEL (12 articles), the ones combining analytical network process (ANP) and DEMATEL (154 articles), and the ones based on other DEMATEL methods (12 articles). The classification scheme of the DEMATEL articles is shown in Figure 1. Most of the papers on ANP and DEMATEL hybridization are included in a review paper of DEMATEL approaches for criteria interaction handling with ANP by Gölcük and Baykasoğlu [7]. Therefore, in the following sections, we will not discuss the studies which apply the DEMATEL in conjunction with ANP to deal with interactions among criteria.

Figure 1: Classification scheme of the DEMATEL articles.

3. Reviews of DEMATEL Methods

3.1. The Classical DEMATEL

As stated earlier, the DEMATEL technique can convert the interrelations between factors into an intelligible structural model of the system and divide them into a cause group and an effect group [8]. Hence, it is an applicable and useful tool to analyze the interdependent relationships among factors in a complex system and rank them for long-term strategic decision making and indicating improvement scopes. The formulating steps of the classical DEMATEL can be summarized as follows [810].

Step 1 (generate the group direct-influence matrix ). To assess the relationships between factors in a system, suppose that experts in a decision group are asked to indicate the direct influence that factor has on factor , using an integer scale of “no influence (0),” “low influence ,” “medium influence ,” “high influence ,” and “very high influence .” Then, the individual direct-influence matrix provided by the th expert can be formed, where all principal diagonal elements are equal to zero and represents the judgment of decision maker on the degree to which factor affects factor . By aggregating the experts’ opinions, the group direct-influence matrix can be obtained by

Step 2 (establish the normalized direct-influence matrix ). When the group direct-influence matrix is acquired, the normalized direct-influence matrix can be achieved by usingAll elements in the matrix are complying with , and at least one such that

Step 3 (construct the total-influence matrix ). Using the normalized direct-influence matrix , the total-influence matrix is then computed by summing the direct effects and all of the indirect effects byin which is denoted as an identity matrix.

Step 4 (produce the influential relation map (IRM)). At this step, the vectors and , representing the sum of the rows and the sum of the columns from the total-influence matrix , are defined by the following formulas:where is the th row sum in the matrix and displays the sum of the direct and indirect effects dispatching from factor to the other factors. Similarly, is the th column sum in the matrix and depicts the sum of direct and indirect effects that factor is receiving from the other factors.

Let and ; the horizontal axis vector named “Prominence” illustrates the strength of influences that are given and received of the factor. That is, stands for the degree of central role that the factor plays in the system. Alike, the vertical axis vector called “Relation” shows the net effect that the factor contributes to the system. If () is positive, then the factor has a net influence on the other factors and can be grouped into cause group; if () is negative, then the factor is being influenced by the other factors on the whole and should be grouped into effect group. Finally, an IRM can be created by mapping the dataset of (, ), which provides valuable insights for decision making.

3.1.1. Observations and Findings

Table 1 summarizes all the classical DEMATEL studies based on the particular purpose of using DEMATEL, the topic of decision making, and other methods combined. According to the distinct usage of the DEMATEL method, the current classical DEMATEL researches can be classified into three types: the first type is merely clarifying the interrelationships between factors or criteria; the second type is identifying key factors based on the causal relationships and the degrees of interrelationship between them; the third type is determining criteria weights by analyzing the interrelationships and impact levels of criteria.

Table 1: Various applications of the classical DEMATEL.

In Table 1, we have provided an overview on the existing applications of the classical DEMATEL for solving complicated and intertwined problems in many fields, based on which we now point out some critical steps added to the original approach.

Step 4-1 (set a threshold value to draw the IRM). In the above, the IRM is constructed based on the information from the matrix to explain the structure relations of factors. But, in some situations, the IRM will be too complex to show the valuable information for decision making if all the relations are considered. Therefore, a threshold value is set in many studies to filter out negligible effects. That is, only the element of matrix , whose influence level is greater than the value of , is selected and converted into an IRM.

If the threshold value is too low, many factors are included and the IRM will be too complex to comprehend. In contrast, some important factors may be excluded if the threshold value is too high. In the literature, the threshold value is usually determined by experts through discussions [10, 11], the results of literature review, the brainstorming technique [12], the maximum mean deentropy (MMDE) [13], the average of all elements in the matrix [14], or the maximum value of the diagonal elements of the matrix [15].

Step 4-2 (obtain the inner dependence matrix ). When the total-influence matrix is produced, in [16, 17], an inner dependence matrix is acquired by normalizing the matrix so that each column sum is equal to 1. But, in [18], the inner dependence matrix is derived based on the threshold value and only the factors whose effects in the matrix are larger than are shown in the matrix .

To interpret the results easily and keep the complexity of the system manageable, Tzeng [19] established a simplified normalized total-influence matrix using a normalization method and the threshold value . First, the normalized total-influence matrix is calculated by using (6) to force the values of the matrix within the scope of a measurement scale.where is the highest score for measuring the degree of relative impact between factors and if the integral scale of 0 to 4 is used. Then, the simplified normalized total-influence matrix is obtained by eliminating insignificant effects in the matrix based on the threshold value . That is,

Step 4- (divide the IRM into four quadrants). Once an IRM is acquired, eight of the classical DEMATEL studies classified the factors in a complicated system into four quadrants according to their locations in the diagram. In [2022], the IRM is divided into four quadrants I to IV, as displayed in Figure 2, by calculating the mean of (). The factors in quadrant I are identified as core factors or intertwined givers since they have high prominence and relation; the factors in quadrant II are identified as driving factors or autonomous givers because they have low prominence but high relation. The factors in quadrant III have low prominence and relation and are relatively disconnected from the system (called independent factors or autonomous receivers); the factors in quadrant IV have high prominence but low relation (called impact factors or intertwined receivers), which are impacted by other factors and cannot be directly improved. From Figure 2, decision makers can visually detect the complex causal relationships among factors and further spotlight valuable insights for decision making.

Figure 2: Four-quadrant IRM.

In addition, Wu et al. [23] developed a duo-theme DEMATEL to explore the decisive factors affecting the adoption Software as a Service (SaaS) in an organization. They treated the perceived benefits (PB) and perceived risks (PR) of adopting SaaS solutions as two distinct themes and developed a four-quadrant causal map, called PB-PR matrix, to facilitate decision making (see Figure 3). The primary difference between the duo-theme and the traditional DEMATEL is that the duo-theme DEMATEL combine two IRMs into a single PB-PR matrix by transforming “positive” () value of each factor in PR into “negative” [24].

Figure 3: The PB-PR matrix.

Step 5-1 (net influence matrix). After visualizing the complex causal relationships among factors using the IRM, Wang et al. [25, 26] further developed the net influence matrix to evaluate the strength of influence of one factor on another, in which

Step 6 (calculate the importance weights for criteria). In some studies, the classical DEMATEL technique was used to compute the weights of criteria. Normally, the criteria weights are determined based on the prominence () through a normalization procedure as follows [27, 28]:

To correct for structural relations among criteria, Khazai et al. [29] proposed using the degree of dispatching, , to calculate the dependency weights of criteria:where and .

Then, the overall weight of each criterion is derived bywhere is the importance weight of the th criterion assigned by a group of experts.

3.1.2. Comparison with Other MCDM Methods

In the literature, a lot of effective MCDM methods were developed for dealing with group decision making problems [3032]. In this part, the DEMATEL technique is compared with some other MCDM methods to show its advantages and disadvantages. We choose the most commonly used methods in MCDM, that is, analytic hierarchical process (AHP), grey relational analysis (GRA), technique for order performance by similarity to ideal solution (TOPSIS), VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje), and ELECTRE (ELimination Et Choix Traduisant la REalité), to compare the procedural basis of these MCDM methods.

In the AHP, a hierarchy considers the distribution of a goal among the elements being compared and judges which element has a greater influence on that goal [33, 34]. The GRA is an impact evaluation model that measures the degree of similarity or difference between two sequences based on relation grade [35]. The VIKOR method introduces the ranking index based on the particular measure of “closeness” to the ideal solution by using linear normalization [36]. The basic principle of the TOPSIS is that the chosen alternative should have the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution [37]. The ELECTRE is a prominent outranking MCDM technique, which selects the best action from a proposed set of ones based on multiattribute utility theory [38]. Compared with these MCDM methods, the DEMATEL technique has the following advantages: It effectively analyzes the mutual influences (both direct and indirect effects) among different factors and understands the complicated cause and effect relationships in the decision making problem. It is able to visualize the interrelationships between factors via an IRM and enable the decision maker to clearly understand which factors have mutual influences on one another. The DEMATEL can be used not only to determine the ranking of alternatives, but also to find out critical evaluation criteria and measure the weights of evaluation criteria. Although the AHP can be applied to rank alternatives and determine criteria weights, it assumes that the criteria are independent and fails to consider their interactions and dependencies. The ANP, an advanced version of the AHP, can deal with the dependence and feedback between criteria; but as indicated in [3941], the assumption of equal weight for each cluster to obtain a weighted supermatrix in the ANP is not reasonable in practical situations.

On the other hand, in comparison to other MCDM methods, the possible disadvantages of the DEMATEL technique may be the following: It determines the ranking of alternatives based on interdependent relationships among them; but other criteria are not incorporated in the decision making problem. The relative weights of experts are not considered in aggregating personal judgments of experts into group assessments. It cannot take into account the aspiration level of alternatives as in the GRA and VIKOR methods or obtain partial ranking orders of alternatives as in the ELECTRE approach. Therefore, the DEMATEL has been integrated with other MCDM methods to combine their desired properties in the literature. Next, we will discuss the situations in which it is more appropriate to use the DEMATEL method before some other methods.

3.1.3. Combination with Other Methods

Analyzing the data contained in Table 1, we can observe that the crisp DEMATEL has been combined with a variety of other methods or tools to solve the management decision problems effectively, and the methods most frequently integrated with the DEMATEL include AHP, balanced scorecard (BSC), TOPSIS, and quality function deployment (QFD). Generally, the classical DEMATEL are applied to the following circumstances in combination with other methods. First, it can be used to identify the interdependency among dimensions or perspectives. For example, the DEMATEL was applied to determine the interrelationships between four BSC perspectives [16] and to unveil the implicit interrelationships of customer requirements [210]. Second, it can be used to calculate the weights of evaluation criteria. For instance, the DEMATEL was employed to resolve criteria interdependency relationship weights and then the TOPSIS is utilized to evaluate the service quality of hot spring hotels [122]. Third, it can be used to determine critical factors or criteria via analyzing their dependent relations. For example, the DEMATEL method was applied first to select the most important sustainable criteria, and fuzzy AHP is constructed next to rank end-of-life vehicle management alternatives [108].

3.2. Fuzzy DEMATEL

In the original DEMATEL, the relationships of decision factors are assessed by crisp values so as to establish a structural model. However, in many real-world applications, human judgments are often unclear and exact numerical values are inadequate to estimate the vague interdependency relationships between criteria. Hence, the concept of fuzzy sets [214] has been applied to the DEMATEL method by many researchers. The fuzzy DEMATEL papers identified in this literature survey are summarized in Table 2 for the convenience of reading and understanding. This table also gives the classification of such papers based on different purposes of using the fuzzy DEMATEL. Generally, two types of fuzzy DEMATEL model have been put forward in the literature, that is, fuzzy logic and DEMATEL and fuzzy-based DEMATEL, which will be outlined briefly in the following.

Table 2: Various applications of fuzzy DEMATEL.
3.2.1. Fuzzy Logic and DEMATEL

In this model, fuzzy logic and DEMATEL are combined in a decision model but implemented independently. This model first employs fuzzy sets to handle the experts’ vague judgments and assessments on impact levels between factors and converts fuzzy numbers into crisp values for the group direct-influence matrix and then performs the classical DEMATEL procedure. Based on the basic definitions and operations of fuzzy sets, the following fuzzy logic and DEMATEL methodology was developed [130132].

Step 1. Evaluate the mutual influences between factors using fuzzy linguistic scale.
In this step, it is necessary to establish a fuzzy linguistic scale to assess the causal relationships among factors. In order to tackle the vagueness and imprecision in human assessments, the linguistic terms “No, Very Low, Low, High, Very High” expressed in triangular fuzzy numbers can be used for the linguistic variable “influence.” As a result, the individual direct-influence fuzzy matrix is acquired for each of the respondents , where is the fuzzy assessment of expert regarding the influence degree between factors and .

Step 2. Aggregate the assessments of experts and set up the group direct-influence fuzzy matrix .
After constructing the individual matrixes , we can calculate the group direct-influence fuzzy matrix via aggregating all the experts’ judgments, where can be viewed as a triangular fuzzy number and is derived by

Step 3. Transform the group fuzzy assessments into crisp values and form the group direct-influence matrix .

Using a defuzzification method, the group direct-influence fuzzy matrix can be defuzzified as a group direct-influence matrix . Or according to the CFCS (converting fuzzy data into crisp scores) method [215], the fuzzy assessments of experts on the pairwise relations between factors can be defuzzified and aggregated into crisp scores to construct the group direct-influence matrix [126, 130, 132, 134, 136, 137, 139, 142144, 147149, 152].

Step 4. Apply the classical DEMATEL approach to(i)establish the normalized direct-influence matrix ,(ii)construct the total-influence matrix ,(iii)produce the IRM.

From the group direct-influence matrix , the normalized direct-influence matrix can be arrived at by (2). Then, the total-influence matrix is obtained through (4). Finally, an IRM can be constructed by using (5), with the horizontal axis () and the vertical axis ().

3.2.2. Fuzzy-Based DEMATEL

In this extended model, fuzzy logic is first employed to deal with the vagueness and imprecision involved in the influence degree estimation, then the DEMATEL analysis is completed, and finally the resulting fuzzy numbers are converted into numerical values for making decisions. The analytical procedure of fuzzy-based DEMATEL model is described as follows [159, 171].

Step 1. Evaluate the relationships between factors using fuzzy linguistic scale.

Step 2. Establish the group direct-influence fuzzy matrix .

Step 3. Generate the normalized direct-influence fuzzy matrix bywhereAt least one is assumed such that Note that, in some studies [157, 159, 160, 162, 166, 176], the individual direct-influence fuzzy matrixes are normalized first and then aggregated via arithmetic mean to get the normalized direct-influence fuzzy matrix . In addition, formula (16) was utilized to normalize the group direct-influence fuzzy matrix in [156, 161, 168, 172, 178, 179, 181, 183].

Step 4. Obtain the total-influence fuzzy matrix byHere andin which , and is an identity matrix. The elements of triangular fuzzy numbers in the matrix are divided into , and , and , when for any .

Step 5. Produce the IRM.
Once the total-influence fuzzy matrix is obtained, then and can be calculated easily in which and are the sum of rows and the sum of columns within the matrix , respectively. Next, the fuzzy numbers of and are converted into crisp numbers by using a defuzzification method. A causal diagram can be drawn like the classical DEMATEL by mapping the ordered pairs of and .

In the above, the fuzzy numbers are not transformed until after calculating the prominence degree and the net effect . But a defuzzification step was implemented in Step by some researchers [161, 179, 181, 182] to defuzzify the total-influence fuzzy matrix into the total-influence matrix . The rest of the steps are the same as the original DEMETAL technique.

Generally, triangular fuzzy numbers were utilized in the fuzzy DEMETAL studies except [129, 177]. In [177], the authors developed an extension of fuzzy DEMATEL to trapezoidal membership functions to analyze the complex cause-effect relationships between variables in a composite indicator for disaster resilience. In [129], the authors employed a fuzzy DEMATEL methodology using trapezoidal fuzzy numbers for evaluating the enablers in solar power developments in India.

3.2.3. Observations and Findings

(1) Defuzzification Methods. In the fuzzy DEMATEL literature, a variety of defuzzification methods have been employed for the factor interrelation analysis. Considering that the defuzzification of fuzzy numbers is very vital for the DEMATEL methodologies combined with fuzzy logic, we here conduct a survey on the defuzzification algorithms used in the fuzzy DEMATEL studies.

The CFCS method suggested by Opricovic and Tzeng [215] is the most prevalently adopted defuzzification algorithm in the fuzzy logic and DEMATEL models. For the fuzzy influence assessment given by expert , the defuzzification procedure based on the CFCS is performed as follows [130, 136, 138, 215, 216].

Step 1. Normalization of the fuzzy numbers:

Step 2. Compute left and right normalized values:

Step 3. Compute total normalized crisp value:

Step 4. Compute crisp values:Then, the different judgments of experts are integrated to construct the group direct-influence matrix by

In the fuzzy-based DEMATEL methods, the following CFCS method was applied to calculate the prominence and the relation [159, 162, 164, 167]:where denotes the defuzzified value of the fuzzy number and .

The centroid method (center-of-gravity (COG) or center of area (COA)) was used to determine the crisp values of fuzzy numbers in [131, 158, 165, 170, 179]. For the triangular fuzzy number , its crisp value can be found with the following equivalent relations:

In [180, 184], the signed distance of a fuzzy number (called signed distance method or Yager ranking method in [182]) shown in (29) was used as its defuzzified value. Patil and Kant [141] defuzzified each fuzzy number into a crisp value by using the graded mean integration representation method as (30). In [176], the defuzzification of fuzzy numbers is carried out using (31) to compute the point that divides the area of a fuzzy set into two equal parts.

(2) Weighting Methods. As shown in Table 2, many studies have applied the fuzzy DEMETAL to determine the weights of criteria considering their hierarchies, and a variety of weighting methods have been suggested. In addition to those methods already mentioned in the classical DEMETAL studies, that is, those based and dependency weights, some new weighting methods have been developed.

The vector length method has been used in [150, 176, 180, 184], which sets the importance of criteria with the following formula:Then the weight of any criterion can be normalized as follows:

Wang [179] evaluated the importance weights of criteria by normalizing their absolute relation values:Here represents a signed relation value for the th criterion.

Besides, based on the interactions among criteria, fuzzy AHP was utilized by Wang and Wu [181] and Hsu et al. [171], fuzzy ANP was used by Taşkin et al. [186], Fetanat and Khorasaninejad [182], and Bakeshlou et al. [154], and fuzzy DEMATEL-based analytic network process (DANP) was employed by Hu et al. [183] to calculate relative weights of criteria.

3.3. Grey DEMATEL

Grey theory [35] is a mathematical theory proposed to cope with systems which lack information. It is an effective methodology to resolve uncertain and indeterminate problems and is superior in theoretical analysis of systems with discrete data and incomplete information. Hence, grey theory has been incorporated with the DEMATEL by some researchers for the evaluation of factor intertwined relations in real-life systems. To facilitate reading and comparison, the reviewed twelve grey DEMATEL studies are summarized in Table 3. All of them adopted grey DEMATEL methods for the identification of key factors through analyzing the interaffected relationships among them.

Table 3: Applications of grey DEMATEL.

Similar to the fuzzy DEMATEL, there are mainly two types of grey DEMATEL methods, that is, the grey theory and DEMATEL and the grey-based DEMATEL. Fu et al. [187] first introduced the grey theory and DEMATEL methodology to investigate the importance of green supplier development programs at a telecommunications systems provider. The proposed method involves assessing interdependency relationships among factors by a grey linguistics scale, transforming grey numbers into single real numbers using a modified CFCS process, and eventually executing the classical DEMATEL steps to obtain an IRM with associated analysis. Later, the grey theory and DEMATEL method was applied by Dou and Sarkis [188] to evaluate the barriers of implementing China RoHS (the restriction of the use of hazardous substances in electrical and electronic equipment) regulations from a multiple stakeholder perspective, by Zhu et al. [189] to identify the supply chain-based barriers for truck-engine remanufacturing in China, by Rajesh and Ravi [190] to ascertain the major enablers of supply chain risk mitigation in electronic supply chains, by Shao et al. [191] to analyze the barriers between environmentally friendly products and consumers on the European automobile industry, by Govindan et al. [192] to develop important criteria for third-party logistics provider selection and evaluation, and by Xia et al. [193] to analyze the internal barriers for remanufacturers in the Chinese automotive sector.

Bai and Sarkis [194] argued that the data conversion process of the grey and DEMATEL method will cause a loss of original decision information, thus leading to unreasonable or misleading results in the final decision. Accordingly, they proposed a grey-based DEMATEL model to identify critical success factors (CFSs) in the successful implementation of business process management (BPM). In their integrated structural model, the authors evaluated various BPM implementation CSFs directly through the grey-based DEMATEL and did not “degrey” the grey numbers until after calculating the prominence and relation indexes. Liang et al. [195] also reported a grey-based DEMATEL for identifying the CFSs for promoting sustainable development of biofuel industry in China.

Additionally, Tseng [196] proposed a grey-fuzzy DEMATEL approach based on a grey possibility degree to deal with real estate agent service quality expectation ranking with uncertainty. Su et al. [197] developed a hierarchical grey DEMATEL methodology for improving sustainable supply chain management under hierarchical structure interrelationships and incomplete information. Ozcan and Tuysuz [197] elaborated upon a grey-based multicriteria performance evaluation model for retail stores by integrating DEMATEL and GRA methods.

It is worth noting that different from the threshold determination methods mentioned in the traditional DEMATEL part, the threshold value in the grey DEMATEL papers was usually yielded based on the mean () and standard deviation () of the values from the total-influence matrix . For example, in [187, 191, 193, 194], the threshold is set up by computing the sum of the mean and standard deviation (). Rajesh and Ravi [190] set the threshold value by adding 1.5 times the standard deviation to the mean () and Zhu et al. [189] added two standard deviations to the mean () to calculate the value of .

3.4. Other DEMATEL Methods

In previous sections, we have overviewed the DEMATEL for decision making under different contexts, that is, the original crisp DEMATEL, the fuzzy DEMATEL, and the grey DEMATEL. Recently, various approaches that combine other new uncertain theories with DEMATEL have been put forward to enhance its analysis capability and practicality. Table 4 shows those modifications identified in the literature and, in the sequence, a detailed literature analysis is given.

Table 4: Applications of other DEMATEL.

Jenab et al. [199] proposed an interval DEMATEL (i-DEMATEL) method for evaluating and implementing computer integrated manufacturing technologies that takes into account all decision parameters. Abdullah and Zulkifli [200] reported an interval type 2 fuzzy DEMATEL (IT2-fuzzy DEMATEL) and combined it with fuzzy AHP for human resource management, where interval type 2 trapezoidal fuzzy numbers were used to resolve the relationships among dimensions and criteria. Nikjoo and Saeedpoor [201] presented an intuitionistic fuzzy DEMATEL approach to determine the key components of strengths, weaknesses, opportunities, and threats (SWOT) matrix, and Govindan et al. [202] used the DEMATEL method with intuitionistic fuzzy sets (IFSs) to handle the important and causal relationships between green practices and performances in green supply chain management. Fan et al. [203] developed an extended DEMATEL method using 2-tuple fuzzy linguistic representation model to identify risk factors of IT outsourcing, and Liu et al. [204] utilized a 2-tuple DEMATEL technique to compute the importance weights of criteria and proposed a hybrid MCDM model for evaluating health-care waste treatment technologies.

Suo et al. [205] presented an extension of DEMATEL method in an uncertain linguistic environment, which allows the judgments on the correlations between factors in the form of uncertain linguistic terms. Li et al. [206] proposed an evidential DEMATEL method for identifying CFSs in emergency management, in which the evaluations of influencing factors expressed in intuitionistic fuzzy numbers (IFNs) were transformed into basic probability assignments (BPAs) and Dempster-Shafer (D-S) theory was used to obtain the group assessment BPA matrix. Chang and Cheng [207] suggested an efficient algorithm which combines IFSs and the DEMATEL to evaluate the risk of failure modes and Chang [208] proposed a risk ranking model integrating soft set theory and the DEMATEL technique for the risk assessment in failure mode and effect analysis (FMEA). Geng and Chu [209] dealt with the uncertainty and vagueness of expert evaluations by using vague sets and presented a revised DEMATEL approach to capture the mutual influence relationships among quality attributes. Then, a new importance-performance analysis (IPA) method for customer satisfaction evaluation was proposed based on Kano model and vague DEMATEL. Wu et al. [210] presented an integrated analytical model for QFD, in which hesitant fuzzy DEMATEL was adopted to analyze the interrelationships among customer requirements and determine their weights.

4. Bibliometric Analysis

Based on the collected papers on the DEMATEL, a bibliometric analysis is conducted in this section regarding quantity of articles published per year, application areas of DEMATEL, and the highly cited papers. The intention of this bibliometric analysis is to find out current research trends, distribution of the articles in different categories, and interactions with other fields, which provide valuable insights for researchers and practitioners working in this field. First, from Figure 4, one can observe that the number of publications on DEMATEL has increased considerably, especially after the year 2009. It can be expected that the studies of utilizing the DEMATEL and its variants will continue to grow at an increased pace in the coming decade. Figure 4 also shows the trend in the number of publications in each category. It can be found that the classical and the fuzzy DEMATEL methods are mostly used for decision making in the earlier literature. It was only after the year 2010 when the focus shifted to employing the combination of ANP and DEMATEL. However, the usage of the classical and the fuzzy DEMATEL methods has continued to grow until more recently when some papers began to deal with the grey and other DEMATEL applications. Normally, if the relationships of systems are given by crisp values in establishing a structural model, the classical DEMATEL can be used for evaluating problems and decision making [217]. For the cases that the human judgments about preferences are unclear and hard to estimate by exact numerical values, the fuzzy DEMATEL is necessary for making better decisions in fuzzy environments. The grey DEMATEL can be applied to the systems with limited data and incomplete information, which may exhibit random uncertainty.

Figure 4: Distribution of articles according to the years.

From Figure 5, we can see that the DEMATEL and its various improvements have been widely used in a lot of areas, practically in computer science (40.6%), engineering (35.7%), business and managements (26.4%), decision sciences (17.7%), and social sciences (15.5%).

Figure 5: Distribution of articles according to application areas.

In Table 5, the top ten papers are given by analyzing the total citation and average citation of each publication. “Total citation” refers to the number of Scopus citations for a paper until 2016, and “average citation” or called “citation per year” is equal to the total citation divided by the number of years from publication. It can be seen that the most influenced papers in this filed are Tzeng et al. [10], Wu and Lee [130], Lin and Wu [159], Wu [211], Huang et al. [8], and Büyüközkan and Çifçi [212]. Note that the ranking of articles based upon the total citation does not necessarily match the average citation ranking. Besides, it can be observed that all the highly cited studies are at least five years old except Büyüközkan and Çifçi [212]. This is because sufficient time is usually needed for an influential paper to establish citations.

Table 5: The top ten papers based on citation measures.

5. Conclusions and Suggestions for Future Work

In recent decade, the DEMATEL technique has attracted a lot of attention from both practitioners and researchers and has been used in a wide range of areas due to its ability to handle complex relationships between components of a system. In this paper, a representative and comprehensive review on the DEMATEL methods and applications from 2006 to 2016 was provided. According to the distinct forms of the DEMATEL used in the selected publications, five categories are identified and carefully investigated along with their main steps and characteristics. This review uncovers the current state of the research on this area based on statistical analysis results of the DEMATEL literature. It can be expected that the number of approaches and applications of the DEMATEL will continue to grow in the future due to its distinguished power and the increasing complexity of decision making problems.

Through the detailed review regarding the DEMATEL methodologies, the following possible future research directions for both theory and applications are suggested. First, to represent uncertainty and vagueness within the decision making process, the original DEMATEL was mainly combined with fuzzy sets and grey theory and only a few studies applied other uncertain theories, such as interval type 2 fuzzy sets, IFSs, 2-tuples and uncertain linguistic terms, to improve the DEMATEL recently. In the future, investigating the combination of DEMATEL with more advanced uncertain theories, such as hesitant fuzzy linguistic term sets and cloud model theory, for better decisions in uncertainty would be interesting. Second, the relative weights of decision makers are assumed to be equally important in computing the group direct-influence matrix . However, in practical situations, decision makers usually come from different specialty fields and each expert has unique characteristics with regard to knowledge, skills, experience, and personality, which implies that different expert weights should be assigned to reflect their influences on final analysis results. Moreover, in the interrelationship evaluation process, some decision makers may assign unduly high or unduly low preference values to their “preferred” or “repugnant” factors. Thus, in the future, advanced DEMATEL methods should be developed to relieve the influence of unfair arguments on the decision results. Third, proposing more objective and effective methods is required to set the crucial parameters in DEMATEL such as threshold value and criteria weights in further research. For example, although different methods have been suggested to determine the value of in current DEMATEL studies, these methods are subjective and time-consuming [218].

From the perspective of applications, our study also has several implications for further research. First, the literature review shows that a series of modified DEMATEL approaches have been developed, but no or few studies have been done to compare between the methods in the same or different groups. So, one recommendation for future research is the evaluation and comparison of the advantages and drawbacks of different DEMATEL methods in order to aid practitioners to select the suitable one for the problem to be solved. Second, to analyze the complicated interrelations between factors accurately, many computations are involved in the extended DEMATEL models, which limit their applications. Thus, a software tool should be developed in the future to facilitate the implementation of the DEMATEL technique. Finally, future research could apply the DEMATEL methodology and its variants to other situations and broader fields that are not considered in the previous studies.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (nos. 61773250 and 71402090), the Shanghai Pujiang Talents Program (no. 15PJC050), and the Program for Professor of Special Appointment (Young Eastern Scholar) at Shanghai Institutions of Higher Learning (no. QD2015019).

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