Extension card · Fuzzy
Scenario fuzzy SWARA
This is the form of SWARA for situations where criteria's successive importance differences are given as triangular fuzzy numbers. It applies crisp SWARA separately to the triangle's lower, middle and upper end and averages the three weight vectors; the output is not a ranking but a weight vector summing to 1.
Base method
SWARA →
Philosophy, mechanics, strengths and weaknesses are on the base method card; this card describes only the difference.
Data type (family)
Fuzzy →
What this data type is, when to use it, how to write it in a cell: the family's full account is here.
What Changes from the Base Method?
Input. In crisp SWARA, each criterion's relative importance difference from the one before it (s_j) is a single number. Here this difference is a triangular fuzzy number (lower, middle, upper); the most important criterion's reference difference, exactly as in crisp SWARA, is always zero, entered here as (0; 0; 0).
Calculation path. Vrtagić and colleagues' (2021) Fuzzy SWARA (see the Fuzzy SWARA card) proceeds with triangular arithmetic: the coefficient and the interim weight are calculated as triangles, and defuzzification happens at the end. This profile does not work that way. All of crisp SWARA's steps (coefficient = 1 + s_j, interim weight = the previous one divided by the coefficient, normalisation) are run three times, independently of one another: once on the lower-end differences, once on the middle values, once on the upper-end differences; the three weight vectors are then averaged criterion by criterion and renormalised to sum to 1. Uncertainty is not carried through triangular arithmetic; it is processed from the start as three separate scenarios and combined only at the end by averaging.
Separate normalisation. Each component's (lower, middle, upper) own resulting weight vector is normalised to sum to 1 within itself before being combined. When the three normalised vectors are averaged, the total naturally comes out at 1 again. DecisionMind also calculates the gap between the averaged weight and the weight coming from the middle component alone; this is a measure of how much the fuzziness has changed the weight, and a degeneracy warning is flagged if the three components give exactly the same weight.
SWARA's non-linearity produces a different outcome from SMART. In Fuzzy SMART (see the Fuzzy SMART card), importance scores are directly proportioned; if the score bands are scaled up or down proportionally, that is, by the same factor, the three bands give exactly the same weight. SWARA's coefficient formula (1/(1+s_j)) is not linear; even if successive differences are scaled up or down proportionally, the weights produced by the three components do not come out identical. In the illustrative example below, the differences are exactly proportional (lower = middle × 0.8, upper = middle × 1.2), and yet the three components still give different weights.
DecisionMind fixes, in this profile, the independent component-based SWARA computation and the final average-then-renormalise rule.
How to Read the Output
The weight, as in base SWARA, shows a criterion's relative importance against the others within the given ranking and set of successive comparisons; the weights always sum to 1. No version of SWARA has an independent consistency indicator; this profile does not close that gap either.
The difference is here. This weight is a DecisionMind-specific profile, produced by calculating three independent scenarios (pessimistic, middle, optimistic) separately and averaging them. It cannot be compared directly with Vrtagić and colleagues' (2021) triangular-arithmetic-based Fuzzy SWARA. There, uncertainty is carried as a single triangle right through to defuzzification; here the three points are processed from the start as three independent calculations.
Thus instead of writing:
"This weight is a standard Fuzzy SWARA result from the literature"
the report should read:
"This weight is a DecisionMind-specific profile, produced by calculating three scenarios (lower, middle, upper) independently and averaging them; it cannot be compared directly with Fuzzy SWARA results based on triangular arithmetic"
When to Prefer This over the Base Method
Today this profile cannot be recommended in DecisionMind's live product, because the engine does not yet run this method. Mechanically, it is designed for cases where the expert thinks of the successive importance difference as three separate numbers, pessimistic, middle and optimistic, and simply wants these three scenarios calculated independently and then averaged. It can be considered for a use case that wants a three-point sensitivity reading without the extra complexity that triangular arithmetic (Fuzzy SWARA) brings.
Opening up a measured difference into a triangle is producing uncertainty, not modelling it; this principle holds here too. SWARA's exit condition also applies here: if the expert is not sure of the criteria's correct ranking, this profile does not test that uncertainty either.
Mistakes Specific to This Extension
Presenting this as a standard Fuzzy SWARA. The manifest explicitly states that this profile does not rest on a canonical source; it must not be introduced in the report as "the Fuzzy SWARA in the literature," and should instead be pointed to the genuinely sourced Fuzzy SWARA card.
Entering the most important criterion's reference difference as anything other than (0;0;0). This rule applies identically in all three components; if it is violated in even one component, that component's SWARA chain is built wrong from the start.
Averaging the components before calculating them separately. Averaging the three triangles' lower-middle-upper values first and then running a single crisp SWARA gives a different result; this profile is defined as averaging three independent SWARA calculations afterwards, not averaging the input beforehand.
Presenting this method to the user as an option that can be run through the product today. DecisionMind's current version rejects this method for lack of a canonical engine; until that situation changes, it must not be written into a report as a "usable method."
The governing principle is this:
This profile has no founding paper; it is DecisionMind's own derivation and cannot currently be run within the product. The card documents only what is computed at code level, through an independently run kernel.
Cases
The first case is taken from DecisionMind's source-reproduction record. This record is not a literature example; it is the engine's own test fixture, verified against a pinned analyse_asisance source copy. Because the product API rejects this method today, the figures were produced independently by calling the kernel file directly in Python rather than through the engine's API. The second case is an illustrative construction.
1. Illustrative example (DecisionMind's test record): Scenario-based weighting of three criteria
A publisher's editorial board will weight three criteria before assessing three book proposals for a new series: potential reader interest, translation/rights cost, and fit with the publication schedule. The board has ranked these criteria (reader interest > cost > schedule fit) and has given the successive differences as a pessimistic, middle and optimistic three-point estimate.
| Rank | Criterion | Importance difference from the one before (lower; middle; upper) |
|---|---|---|
| 1 | Potential reader interest | (0; 0; 0) |
| 2 | Translation/rights cost | (0.08; 0.10; 0.12) |
| 3 | Fit with publication schedule | (0.16; 0.20; 0.24) |
The method runs these three differences through three independent SWARA chains (lower, middle, upper), normalises each chain's weight vector within itself, then averages the three.
| Criterion | Lower component | Middle component | Upper component | Average weight |
|---|---|---|---|---|
| Potential reader interest | 0.3671 | 0.3750 | 0.3827 | 0.3749 |
| Translation/rights cost | 0.3399 | 0.3409 | 0.3417 | 0.3408 |
| Fit with publication schedule | 0.2930 | 0.2841 | 0.2756 | 0.2842 |
The result reads as follows. Potential reader interest carries the highest weight in all three components (around 37.5 per cent), and fit with the publication schedule the lowest. The weights the three components produce are close to one another but not exactly identical; this is the ground for the board's hesitation.
The board's hesitation is this: the three differences entered are exactly proportional (lower = middle × 0.8, upper = middle × 1.2), that is, they look like a "proportional fuzzification" of the kind seen in Fuzzy SMART. Yet the three components do not give exactly the same weight, because SWARA's coefficient formula (1/(1+s_j)) is not linear; the reader-interest criterion's weight comes out at 0.3671 in the lower component and 0.3827 in the upper component, a gap of 0.0156. If the differences are widened further (for instance, entering a disproportionate band such as 0.05-0.10-0.25 for the second criterion), this gap grows (when calculated independently, the reader-interest weight spreads between 0.3606 and 0.4090). The board should read this widening as a margin of uncertainty, not present it as a single precise percentage.
In the report: "Averaged across the three scenarios (lower, middle, upper), potential reader interest is the most important criterion at a weight of 37.5 per cent. This weight is a DecisionMind-specific, component-based profile and should not be compared with Fuzzy SWARA results based on triangular arithmetic; this method also cannot currently be run through the product, and the record documents only the engine's behaviour at code level."
Source: DecisionMind's source-reproduction record (manifest J, verified against a pinned analyse_asisance source copy), not a literature example. The weights were independently computed by this card's author by calling the kernel file directly in Python, and matched the manifest's recorded result (C1=0.37493; C2=0.34084; C3=0.28423, 1e-11 tolerance) exactly.
2. Publishing: A journal editorial board weighting article-acceptance criteria
An academic journal's editorial board will weight three criteria used to screen incoming articles: methodological soundness, originality of contribution to the field, and quality of writing and presentation. The board has ranked these criteria (methodological soundness > originality > presentation quality) and, because the board members were not in full agreement, has set the successive differences with a pessimistic-middle-optimistic three-point estimate.
The method runs independent SWARA chains on the three components and averages them. Suppose the result gives methodological soundness the highest weight.
The board's hesitation is this: if the weights produced by the three components diverge noticeably from one another (the degeneracy warning is not flagged), this also indirectly shows how much the board members agree on the successive importance difference. The board should record in its minutes not only the average weight but also the gap between the three components.
In the report: "Methodological soundness receives the highest weight in the average of the three scenarios. The gap between the components has been recorded separately, as an indicator of the board members' disagreement over the successive importance difference; this method cannot yet be run through the product."
3. What Not to Do
The first error is averaging the illustrative example's three triangles up front, that is, reducing the lower, middle and upper values to a single number, and then running crisp SWARA; this differs from this profile's definition and conceals the real gap between the three scenarios. A second error is comparing the weights this profile produces with Vrtagić and colleagues' (2021) Fuzzy SWARA as if they were the same method; the two are different calculation paths. A third error is offering this method to the user within DecisionMind's product today; the engine rejects this method for lack of a canonical engine.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/scenario-fuzzy-swara
This extension has no founding paper in the literature; it has been derived from DecisionMind's internal reference implementation (see the explanation above).
Keršulienė, V., Zavadskas, E. K., & Turskis, Z. (2010). Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management, 11(2), 243–258. DOI: 10.3846/jbem.2010.12
Vrtagić, S., Softić, E., Subotić, M., Stević, Ž., Dordevic, M., & Ponjavic, M. (2021). Ranking road sections based on MCDM model: New improved fuzzy SWARA (IMF SWARA). Axioms, 10(2), 92. DOI: 10.3390/axioms10020092
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. DOI: 10.1016/S0019-9958(65)90241-X