Methods · Ranking
WINGS (Weighted Influence Non-linear Gauge System)
WINGS measures, within a system built from components that influence one another, how central each component is and whether it stands mainly as an influencer or as something influenced.
Base method's data type: Classical
What Is the Method?
WINGS is a method for when your components are not independent of one another ("this risk factor triggers that one," "this project component is entangled with that one") and you want to evaluate them not one by one but through their effects on each other. Its input is a table showing each component's own internal strength and how strongly it affects the other components. Its output is a single "engagement" score for each component, an importance ranking derived from that score, and a weight vector derived in turn from the ranking. WINGS does not sort alternatives into "suitable / unsuitable," nor does it rank alternatives; it shows which part of a system is driving the system and which part is being driven. Michnik proposed it in 2013, and it is regarded as a sibling of the DEMATEL method: both answer the same question, "how is importance measured when components influence one another," with a different calculation.
The Philosophy Behind It
The idea behind WINGS is this. No component in a system stands alone; each both influences others and is influenced by them. Understanding a component's importance requires looking not only at its own strength but at its position within the network.
WINGS captures this with two numbers. Engagement is a component's total volume of interaction. Role tells you the direction of that interaction: whether the component stands predominantly as a cause or predominantly as an effect.
What sets WINGS apart from DEMATEL is that it feeds a component's own internal strength directly into the table. DEMATEL looks only at inter-component influence; WINGS adds the component's own weight to that and normalises against the total of the whole table. This difference explains the "non-linear gauge" part of the name: given the same influence table, WINGS can produce a different ranking from DEMATEL once the internal-strength values change. This method makes no selection; it recognises a system's structure, and its result is generally used as input to another method, such as criterion weighting.
How It Works
The method proceeds in four steps.
First, building the strength matrix. Every off-diagonal cell carries how strongly one component affects another. The diagonal carries each component's own internal strength, that is, its importance independent of anything external. These two pieces of information sit together in a single table.
Second, normalisation. WINGS divides the entire table by the sum of all the values in it. Every cell then falls between 0 and 1, and the table becomes comparable even across different experts working on different scales.
Third, building the total-relation matrix. The normalised table carries only direct effects. WINGS adds indirect effects to this: where A affects B, and B affects C, it also accounts for A's indirect share of the effect on C. This is done through an operation equivalent to the infinite sum of the normalised table, producing a single total-relation matrix.
Fourth, reading engagement and role. In the total-relation matrix, each component's row sum gives how much it affects the others, and its column sum how much it is affected by them. The sum of these two gives engagement; their difference gives role. Weights are derived from engagement.
The formulas behind the steps, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.
How to Read the Output
A component with a high engagement score holds a central position in the system. It both influences a great deal and is influenced a great deal; a change in this component spreads to the rest of the system. A component with low engagement sits at the system's edge, with limited interaction.
Role carries separate information. A positive role shows the component stands predominantly as a cause; a negative role shows it stands predominantly as an effect. A role near zero means the component's share of influencing and being influenced is balanced.
Thus instead of writing:
"WINGS found the most important component"
the report should read:
"With this influence table, the most central component is this one; its engagement score shows the volume of its interaction within the system, not its value on its own"
Engagement scores are meaningful only for this particular influence table. Add a new component to the table and the total changes, the normalisation changes, and the scores change with it; an engagement score cannot be compared with one from a different influence table.
Data Type and Inputs
WINGS works with crisp data: each cell holds a single influence score given by an expert. This score is usually converted from an ordinal scale (none, low, medium, high, very high, and so on) into a number. DecisionMind holds only the base WINGS method, with no extension.
You need a minimum of two components capable of influencing one another, a directional influence score for every pair of components (A's effect on B can differ from B's effect on A), and a score showing each component's own internal strength. It works comfortably with three to twelve components; beyond that, giving consistent scores becomes harder for the expert. WINGS does not ask for weights, it produces them itself; the weights it produces rest on a different foundation than those from independence-assuming methods such as Entropy or CRITIC, which are built for situations where components are not dependent on one another.
When to Use It, When Not To
WINGS is a sound choice where your components influence one another, that is, where changing one changes the others, and your goal is to understand these components' importance or causal position within the system. Its typical fields of use include risk-factor prioritisation, dependency analysis among project components, and mapping the relationships between negotiation topics.
It should not be used where the components are genuinely independent, or where the goal is to rank alternatives (which supplier, which programme) rather than components. Entropy or CRITIC suffice for independent criteria; ranking alternatives requires a ranking method such as TOPSIS or VIKOR, which WINGS does not substitute for.
Components influence one another, the goal is to see centrality and causal role → WINGS
Components influence one another, the goal is only to produce weights → WINGS or DEMATEL, both candidates
Criteria are independent, the goal is to derive weights from data → Entropy, CRITIC
The goal is ranking alternatives, not components → A ranking method such as TOPSIS, VIKOR
Strengths
WINGS's greatest strength is that it feeds a component's own internal strength into the table as information independent of external effects, a dimension that methods looking only at pairwise influence overlook. It captures indirect effects (such as A affecting C through B) via the total-relation matrix, rather than being confined to direct effects alone. Because it gives engagement and role separately, it answers both "how important" and "important in which direction" together.
Weaknesses
Its limitations stem largely from the nature of the input. Influence scores rest on expert judgement; different experts can score the same relationship differently, and this difference feeds straight through to the result. Computing the total-relation matrix requires the normalised table to satisfy a mathematical condition; if that condition is not met, the method produces no solution. A recent study comparing WINGS with DEMATEL showed that the two methods can give different importance rankings for the same influence table, and that this stems from their difference in normalisation (Zandi, Michna and Michnik, 2027). WINGS also does not, any more than DEMATEL, produce a "correct" weight on its own; the weight it produces is a reflection of the scores experts gave the influence table.
Common Mistakes
The most common mistake is skipping a component's own internal strength (the diagonal) or leaving it at zero arbitrarily; this effectively reduces WINGS to DEMATEL and loses the method's distinguishing contribution. A second mistake is the expert giving influence scores carelessly as the number of components grows; consistent scoring becomes difficult beyond twelve components, and the result loses reliability. A third mistake is reading the engagement score directly as an "importance percentage" and comparing it with a score from a different influence table. A fourth mistake is ignoring role information and looking only at engagement; two components can share the same engagement while one stands as a cause and the other as an effect, and that distinction changes the decision.
The governing principle is this:
A WINGS score is a summary of the influence scores components give one another; if these scores are contested, the engagement ranking is contested too, and the report must show this.
Cases
Each case opens with an influence table, describes in words what the method does to it, and shows how to read the result. The first case is drawn from the method's founding source; its figures are the paper's own. The remaining cases are illustrative constructions.
1. Systems Analysis: An abstract three-component example (Michnik, 2013)
Michnik's founding paper uses an abstract system of three components, C1, C2 and C3, to demonstrate WINGS's mechanics. Each component's own internal strength is given on an ordinal scale: C1 very high (4), C2 medium (2), C3 medium (2). The components also affect one another with the following directional scores: C1's effect on C2 is 1, C1's effect on C3 is 4, C2's effect on C1 is 3, C2's effect on C3 is 2, C3's effect on C1 is 2, C3's effect on C2 is 3.
The method first gathers this information into a single strength matrix: internal strengths on the diagonal, pairwise effects off it. It then normalises the table by dividing it by the sum of all values. It then builds the total-relation matrix, which also captures indirect effects. Finally, it calculates each component's engagement (the sum of its row and column totals).
| Component | Own strength | → C1 | → C2 | → C3 |
|---|---|---|---|---|
| C1 | 4 | × | 1 | 4 |
| C2 | 2 | 3 | × | 2 |
| C3 | 2 | 2 | 3 | × |
The result comes out as follows: C1's engagement is 1.185, C3's is 0.986, C2's is 0.851. The ranking is C1, C3, C2.
The result reads as follows. C1 is both the component with the highest internal strength and one that strongly affects C3; these two traits together place it at the centre of the system. C3, despite affecting C1 moderately and C2 strongly, ranks second; its own internal strength is lower than C1's. C2 ranks third; although it affects C1 strongly, its own internal strength is low and the effect it receives from C1 is limited.
Looking at role, C1's role is close to zero (its share of influencing and being influenced is balanced), C2 stands slightly as a cause, and C3 stands slightly as an effect. The analyst hesitates here: C1 ranking first does not mean it is the "best" component, only that it is the one most engaged in interaction. Had the experts scored C1's effect on C3 more moderately (2 instead of 4), the gap between C1 and C3 would narrow, and the ranking could change.
In the report: "With this influence table, the most central component is C1 (engagement 1.185); C3 (0.986) is a close second, and the gap is sensitive to the score given to C1's effect on C3."
Source: Michnik (2013), §3.2.1, Example 1, Table 1. The engagement values are the paper's own values; this example serves as the validation case for DecisionMind's WINGS engine, and the engine reproduces the same result.
2. Publishing: Prioritising production-process components at a publishing house
A publishing house wants to understand the mutual influence among four components of its book-production process: editorial editing, translation quality control, print scheduling and distribution coordination. The publishing management team scores each component's own internal strength and the influence between components on a 0-to-4 scale; for instance, they judge that a delay in editorial editing strongly affects print scheduling, while distribution coordination affects the others less.
The method normalises the influence table for these four components, builds the total-relation matrix capturing indirect effects too, and calculates each component's engagement. Suppose editorial editing receives the highest engagement, because both its own internal strength is high and it indirectly affects print scheduling and distribution. Print scheduling ranks second, being largely affected by editorial editing.
The team hesitates here: does editorial editing's prominence mean resources should be directed towards it, or does it mean that, if editorial editing is already solid, attention should instead go to the components it affects? Looking at role information, editorial editing is found to stand predominantly as a cause; this suggests resource priority should go not to editorial editing itself but to the print-scheduling process it affects.
In the report: "Editorial editing is the most central component in the system and stands predominantly as a cause; resource priority should go to the print-scheduling process it affects, rather than to this component itself."
3. Library Science: Interaction among service components at a university library
A university library wants to examine the relationship among three components affecting service quality: collection currency, staff advisory quality and digital-access infrastructure. Library management judges that better staff advisory quality makes the digital-access infrastructure more effectively used, and that the digital-access infrastructure in turn makes the currency of the collection more noticeable. These relationships are scored on a 0-to-4 scale.
The method builds the total-relation matrix for these three components and calculates engagement scores. Suppose digital-access infrastructure receives the highest engagement; it is both strongly affected by staff quality and affects how visible the collection's currency is. Staff advisory quality ranks second.
Management hesitates here: the high engagement of digital-access infrastructure does not mean the budget should go there; looking at the role score, this component may be found to stand predominantly as an effect, meaning that an improvement in staff quality also improves digital access. In that case, priority should go to staff advisory quality.
In the report: "Digital-access infrastructure is the most central component, but its role is predominantly that of an effect; priority should go to staff advisory quality, which directly feeds this component."
4. What Not to Do
Had the Michnik example been calculated using only the pairwise effects, without accounting for C1's own internal strength (4), WINGS would effectively turn into DEMATEL, and C1's central position would weaken; this would mean carrying the method's name without its logic. A second error is reading the engagement score as "this component is the best"; engagement shows only the volume of interaction, not the component's quality. A third error is giving C1's effect on C3 a high score (4) without justification, letting the result be driven by it, then presenting the result as "objective"; influence scores are expert judgement, and the report must say so.
Sources
For the formulas behind the steps, the intermediate tables and citation formats (BibTeX, RIS, APA), see the DecisionMind method page: decisionmind.app/library/wings
Michnik, J. (2013). Weighted Influence Non-linear Gauge System (WINGS) – An analysis method for the systems of interrelated components. European Journal of Operational Research, 228(3), 536–544. DOI: 10.1016/j.ejor.2013.02.007
Fontela, E., & Gabus, A. (1974). DEMATEL: Progress achieved. Futures, 6(4), 361–363. DOI: 10.1016/0016-3287(74)90086-x
Michnik, J. (2018). The WINGS method with multiple networks and its application to innovation projects selection. International Journal of Applied Management Science, 10(2), 105–124. DOI: 10.1504/ijams.2018.092077
Zandi, A., Michna, P., & Michnik, J. (2027). A balanced WINGS method for power-influence analysis: Simulation-based comparison with DEMATEL. Expert Systems with Applications, 333, 134147. DOI: 10.1016/j.eswa.2026.134147