DANP (DEMATEL-Based ANP)

DANP is a method for producing criterion weights in situations where criteria are not independent of one another, where one influences another. Its output is a crisp weight vector summing to one; it does not rank, and it does not evaluate alternatives. Proposed as a continuation of classical AHP and ANP by Ou-Yang and colleagues (2008), it was set out under the name by which it is known today, "DEMATEL-based ANP", by Yang and Tzeng (2011). It sees wide use in multi-criteria problems where criteria carry cyclical influence on one another, feeding or weakening each other, particularly in business and technology management.

Classical AHP treats criteria as independent of one another and assigns weight through pairwise comparison. In practice, criteria are rarely independent: in choosing a supplier, "cost" and "quality" affect each other, and one may worsen as the other improves. Rather than ignoring this dependency, DANP measures it first. The DEMATEL step reveals, through an influence matrix, how much each criterion influences the others and how much it is influenced by them. The ANP step places this influence information into a network structure and, by circulating the effects across the network an unlimited number of times (the limit super-matrix), arrives at every criterion's final weight, indirect effects included.

The philosophical consequence is this: DANP abandons the assumption that "criteria are independent of one another" and defines weight as the equilibrium point of an influence network. A criterion's weight depends not only on its own direct importance but on how much it influences the other criteria and how much it is influenced by them. This is a more realistic approach than AHP's, though it is also more complex and demands more data, namely a complete matrix of mutual influence between criteria.

The method proceeds through seven steps.

First, source selection. Criteria are grouped into clusters (dimensions such as "financial", "operational", "customer"). An influence matrix is gathered from experts, either directly at the cluster level or at the criterion level; in the latter case it is reduced to the cluster matrix by averaging within clusters.

Second, the DEMATEL total-influence matrix. Experts' direct-influence scores are averaged, normalised, and turned into a total-influence matrix using DEMATEL's own formula (direct effects plus the infinite sum of indirect effects). This matrix shows how much every criterion influences every other criterion, directly and indirectly.

Third, the cluster-influence matrix. The total-influence matrix is, where necessary, thresholded and divided by its row sums to convert it into cluster-to-cluster influence ratios. These ratios carry the ANP network's information on "how much clusters influence one another".

Fourth, the unweighted super-matrix. Every block of the ANP network structure (the influences running from one cluster's criteria to another cluster's criteria) is normalised within itself so that it sums to one.

Fifth, weighting. Every block is multiplied by the cluster-influence ratio found in the third step. This combines both criterion-level and cluster-level influence information into a single matrix.

Sixth, the limit. This weighted matrix is multiplied by itself repeatedly; the process stops once the resulting matrix stops changing (converges). In certain special cases a single limit does not exist, in which case the average of successive powers is taken.

Seventh, reading the result. Any column of the limit matrix gives every criterion's final weight; this column is normalised to obtain the final weight vector.

The formulas behind each step are given on the DecisionMind DANP method page; this card carries no formulas.

The weight reflects not only a criterion's own standalone importance but its power to influence and be influenced by the other criteria in the network. A high weight means the criterion occupies a central position in the network, influencing many criteria or being fed indirectly by many; a low weight means the criterion sits at the network's edge, relatively isolated. Even if a criterion's direct-influence score is low, DANP can still give it a high weight indirectly if the criteria it influences are themselves heavily weighted; this is information direct comparison in AHP can never capture.

Thus instead of writing:

"DANP showed this criterion to be the most important"

the report should read:

"This criterion carries the most weight, both directly and indirectly, in the influence network; this weight depends on the structure of influence between clusters"

DANP works with crisp, numerical data: pairwise influence scores that experts give on a scale such as 0-4. In DecisionMind, DANP has no separately registered extension member within its own family. You need: a list of criteria grouped into clusters, expert scores for how much every pair of criteria (or every pair of clusters) influences the other, and preferably an average across more than one expert. DANP produces weights, it does not ask for weights from outside. It works comfortably with three to twelve criteria; as the number of criteria grows, the influence matrix demanded of the expert grows quadratically, which sets a practical upper limit.

If a genuine interaction exists between criteria, if a change in one is expected to change another, and ignoring this interaction would mislead the decision, DANP is a suitable choice. If the criteria really are independent of one another, the extra complexity is unnecessary and a simpler method such as AHP or BWM will do. If gathering a complete influence matrix from experts is impractical (too many criteria, limited expert time), DANP's data demands cannot be met and a method requiring less data should be preferred.

Criteria influence one another, and this influence needs to feed into the weights → DANP

Criteria are independent, direct pairwise comparison suffices → AHP, BWM

Interaction exists, but only which criterion influences which (the direction of influence) matters, not the weight → DEMATEL

Data is crisp, and the weight should come from the data's own variability → Entropy, CRITIC

DANP is one of the few weighting methods that explicitly models mutual dependency between criteria; by abandoning AHP's assumption that "criteria are independent", it builds a more realistic network structure. Accounting for indirect effects, a criterion's influence reaching a third criterion through another, by approximating an infinite sum, it captures information that methods looking only at direct effects miss.

The method's greatest limitation is its data demand: asking experts for a complete inter-criteria (or inter-cluster) influence matrix stops being practical once the number of criteria grows. Second, the thresholding in the DEMATEL step, deciding which influences count as "negligible" and are zeroed out, is a subjective decision and can change the result. Third, in certain special structures the limit super-matrix can fail to converge to a single limit and oscillate instead; the averaging solution used in that case is itself an assumption. Fourth, even Yang and Tzeng's (2011) own paper does not fully explain exactly how the cluster-influence matrix (Table 5) is derived from the criterion-influence matrix (Table 3); this has led, in practice, to different computation paths appearing under the same name.

The most frequent mistake is treating DEMATEL's total-influence matrix directly as ANP's unweighted super-matrix; the two are different steps and do not substitute for one another. A second mistake is confusing the weighting step with ordinary matrix multiplication; weighting by the cluster-influence ratio is a special operation performed block by block. A third mistake is, when the (I-D) matrix cannot mathematically be inverted, altering the data to force an inverse; this is a signal of an error, not an obstacle to be bent past by distorting the data. A fourth mistake is confusing the direction of which cluster influences which (row influencing column, or the reverse); this directional error can reverse the weights.

The governing principle is this:

A DANP weight measures a criterion's position in the influence network, not its standalone importance; if the way the network is built (clustering, thresholding, direction) changes, the weight changes too, and these choices must be shown in the report.