DEMATEL (Decision Making Trial and Evaluation Laboratory)

DEMATEL is used when you do not have a decision table comparing alternatives, but do have an expert assessment showing how much criteria or factors influence one another. It is a structural-analysis method. It is not a ranking method: it does not put alternatives in order, it compares criteria. Its output is two figures for every criterion: the total influence it gives and the total influence it receives. Two composite values are derived from these: total engagement and net role. Total engagement shows the criterion's centrality within the system. Net role shows whether a criterion is predominantly a "cause" that gives influence, or predominantly an "effect" that receives it. This second value can, if desired, be normalised and used as a criterion weight as well; DecisionMind supports both uses. Gabus and Fontela developed the method in 1972 as a technical report of the Battelle Geneva Research Centre. Being an institutional report rather than a journal article, it carries no DOI. In application surveys, DEMATEL's own individual share is small; in the survey by Mardani et al. (2015), it accounts for roughly 1.8 per cent of the methods examined. It is used more often alongside other methods, ANP, TOPSIS, VIKOR, to map the dependency between criteria in advance.

The question behind DEMATEL is not "which criterion is most important" but "how does the cause-and-effect network between criteria actually operate." Most methods, TOPSIS and SAW among them, treat criteria as independent of one another. DEMATEL assumes the opposite: criteria influence one another. Ignoring this interaction sets up the weighting and the decision incorrectly. As an analogy, think of drawing a network of influence rather than a family tree. In this network, the question is not "who outranks whom" but "who influences whom, and by how much."

This thinking leads DEMATEL to divide criteria into two roles. The cause group consists of criteria that give more influence than they receive, the ones driving the system. The effect group consists of criteria that receive more influence than they give, the ones the system reacts through. This distinction answers the question "intervening in which criterion produces the highest indirect effect." When a criterion in the cause group is improved, that improvement spreads through the network to criteria in the effect group as well. DEMATEL is, in this sense, neither compensatory nor eliminatory; it is a causal map.

The method proceeds through five steps.

First, the direct-influence matrix. Experts, one or a group, answer the following question for every pair of criteria: "How much does this criterion influence that one?" The answer is given on a scale, from 0 to 4, say. A criterion's influence on itself is undefined, so the diagonal is zero. The result is a square direct-influence matrix.

Second, normalisation. DEMATEL finds the largest of the matrix's row and column sums and divides every value by it. This brings the values down to a shared, comparable scale. This step is necessary so that the matrix does not diverge in the following step.

Third, the total-relation matrix. Here DEMATEL accounts not only for direct influences but for indirect ones too. Chained pathways, such as a criterion influencing a third criterion through a second one, are added into the matrix. This step gathers every indirect pathway between criteria into a single matrix.

Fourth, total influence given and received. The total-relation matrix's row sums (D) give each criterion's total influence on the others, and its column sums (R) give each criterion's total influence received from the others.

Fifth, total engagement and net role. DEMATEL sums D and R (D+R) to find the criterion's total engagement in the system; this value shows the criterion's importance, or centrality. It also subtracts R from D (D−R) to find the criterion's net role. If D−R is positive, the criterion sits in the cause group (giving more influence than it receives); if negative, it sits in the effect group (receiving more influence than it gives). If desired, DecisionMind normalises the D+R and D−R values together to convert them into a criterion weight.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

DEMATEL gives two different pieces of information at once, and they must not be confused with one another. Total engagement (D+R) shows the criterion's centrality in the network. A high value means that criterion both gives and receives a great deal of influence; it is a "busy" junction in the system. Net role (D−R) shows the direction of this engagement. If positive, the criterion is predominantly on the giving side, that is, in the cause group; if negative, it is predominantly on the receiving side, that is, in the effect group. A criterion with high total engagement may sit in either the cause or the effect group depending on its net role; the two figures do not say the same thing. A criterion whose D−R sits very close to zero is a borderline case in which the influence given and received is nearly balanced, and the grouping is not decisive. A small change in expert scores can shift such a criterion from one group to the other.

Thus instead of writing:

"DEMATEL ranked criterion C2 as the most important criterion"

the report should read:

"C2 has the highest total engagement; this does not make it the most important criterion, it makes it the most connected criterion in the system. The sign of the net role (D−R) shows which criteria are causes and which are effects"

DEMATEL does not produce a ranking; it produces a structural map.

DEMATEL works with crisp data. Its input differs from a classical decision table: what is needed is a square influence matrix whose rows and columns are the same criteria, and whose diagonal is zero. Every cell is an expert score, from 0 up to a chosen upper bound. A table of alternatives is not DEMATEL's input. DEMATEL does not rank alternatives; it resolves the relationship between criteria. At least two criteria are required. Between three and twelve criteria works comfortably. With larger sets of criteria, it becomes harder for an expert to score every pair consistently. DecisionMind offers three DEMATEL members alongside the base method: fuzzy and scenario-fuzzy extensions. If your data is linguistic/fuzzy rather than crisp scores, you can use the relevant extension.

If your criteria are not independent of one another, that is, if one influences another, DEMATEL is a fitting choice. It is especially useful when you want to make this interaction visible, to separate which criterion drives the system from which one reacts to it. Decision-makers generally use DEMATEL at the start of a decision analysis, before selecting or weighting criteria. DEMATEL alone does not produce a final ranking.

The situations in which it should not be used are as follows. If your criteria are genuinely independent, that is, do not influence one another, DEMATEL adds needless complexity; an objective weighting method such as Entropy or CRITIC is sufficient on its own. If your aim is to rank alternatives, DEMATEL does not do this; you need to feed the weights it produces into a ranking method such as TOPSIS, VIKOR or SAW. If the number of experts is very small, or if there is wide disagreement among experts, a single influence matrix conceals that disagreement.

Mutual influence exists between criteria and you want to map it → DEMATEL

The aim is criterion weight, criteria can be treated as independent → Entropy, CRITIC (objective) · AHP, BWM, SWARA (subjective)

The aim is to rank alternatives → feed the weights DEMATEL produces into a ranking method (TOPSIS, VIKOR, SAW)

You want to fold the interaction between criteria into both weighting and ranking in an integrated way → DEMATEL-based ANP

DEMATEL's most notable strength is that it explicitly accounts for the dependency between criteria that most methods ignore. By dividing criteria not simply into "important/unimportant" but into "driving the system/affected by the system," it shows where intervention should begin. This is information that a method producing weights alone cannot give. Its output can also be presented visually, as a cause-and-effect diagram, and is easy to explain to a decision-maker. It works comfortably with a small to moderate number of criteria and carries a light computational load.

Its limitations arise from the same structure. First, the result depends directly on expert scores. A different group of experts, or a different scale, 0-3 instead of 0-4, say, can produce a different influence matrix. This in turn leads to a different cause/effect split (Si, You, Liu and Zhang, 2018). Second, as the number of criteria grows, it becomes harder for an expert to score every pair consistently. The method is not practical with large sets of criteria. Third, calculating the total-relation matrix requires the normalised matrix to satisfy a particular mathematical condition. If this condition is not met, the calculation diverges and the result is left undefined (DecisionMind catches this in data validation). Fourth, DEMATEL is not, on its own, a widely used method. In the survey by Mardani et al. (2015), it accounts for roughly 1.8 per cent of the 2000-2014 applications examined. It is mostly used together with other methods, and its results have limited external validity on their own.

The most common mistake is reading the total-engagement value (D+R) directly as an "order of importance" and never examining the net role (D−R). Yet a criterion with a high D+R can be either a cause or an effect. A second mistake is assigning a criterion whose D−R sits close to zero firmly to one group, cause or effect, without looking at its sign. This is a borderline classification and can change direction with small changes in expert scores. A third mistake is presenting DEMATEL's output as a ranking among alternatives; DEMATEL compares criteria, not alternatives. A fourth mistake is reporting a single expert's score as "the group's view." Where there are multiple experts, how the matrices were combined, by a simple or a weighted average, should be stated in the report. Fifth is entering a value other than zero into the diagonal cells; this is meaningless by definition.

The governing principle is this:

DEMATEL produces a structure, not a ranking; D+R shows a criterion's centrality, D−R shows who is a cause and who is an effect, and the two do not substitute for one another.