Extension card · Picture
Picture fuzzy EDAS (Kamber, 2026)
Picture fuzzy EDAS is the form of EDAS used when criterion scores come from a board's or a survey's yes-abstain-no vote distribution. It measures every alternative's position relative to the set's average directly on these three-degree votes.
Base method
EDAS →
Philosophy, mechanics, strengths and weaknesses are on the base method card; this card describes only the difference.
Data type (family)
Picture →
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?
Four things change. The decision logic stays the same.
Cells. In crisp EDAS every cell holds a single number. Here every cell holds three degrees: support, abstention, rejection; their sum cannot exceed 1. This triple comes from a board's or a survey's vote distribution on the same judgement. Weights come from outside, as single numbers, and must sum to 1.
Scale equalisation. Crisp EDAS has no such step to begin with; it measures deviation from the average directly. A similar route is followed here, but the cost-direction criteria are completed first. In every cell of a cost criterion, support and rejection swap places while abstention stays the same; every criterion is thus read in the direction "high support is good." An average solution is then built for every criterion column. This average is not the arithmetic mean of individual numbers; it is a triple computed with the picture fuzzy triples' own aggregation rule (a geometric combination).
Deviation. In crisp EDAS, how far above or below the average an alternative falls is measured directly by the numeric difference. Here, every triple is first reduced to a single score through the difference of support minus rejection; the positive and negative deviations are then computed on this score. If an alternative's score is higher than the average's score, a positive deviation results; if lower, a negative one. Crisp EDAS's logic works exactly the same way; the only difference is that the average and the deviation are built on the picture fuzzy score.
Result and defuzzification. The weighted positive and negative deviations are summed, normalised against each other, and combined into a single assessment score. The result is again a single number between 0 and 1. The uncertainty is not defuzzified beforehand; all three degrees are used both while building the average solution and while computing the score.
DecisionMind fixes, for this member, the construction of the average solution with the picture fuzzy addition rule, and the use of support-minus-rejection as the score function.
How to Read the Output
The assessment score is read as in crisp EDAS: it is not a percentage, it is not compared with a different analysis, and every alternative added to or removed from the set shifts the average. What differs is this: the average solution itself now carries an uncertainty coming from the vote distribution. If every alternative's abstention share on a criterion is high, that criterion's average also comes out with high abstention, and deviations are measured against this average.
Thus instead of writing:
"This alternative is good because it is above the average"
the report should read:
"This alternative is favourably positioned relative to the average built from the set's vote distribution; this average also carries the set's own abstention share"
When to Prefer This over the Base Method
Use this extension when criterion assessments come from a board's, a survey's, or a panel's yes, abstain, no vote distribution on the same judgement, and a position-relative-to-the-set's-average criterion suits your decision. As the Picture Fuzzy data-type card explains, the abstention share must be counted separately; it must not be invented from a single support percentage.
There is no need to expand a measured criterion into a picture fuzzy triple. DecisionMind requires a single data type; if some criteria in the matrix rest on votes and others on measurement, all of them must be written in the same type. The neutrosophic data type also uses a three-degree structure, but there the three degrees are independent of one another and their sum can exceed 1; here the sum cannot exceed 1. The two should not be confused.
The exit condition is the same as for crisp EDAS. If no concession is acceptable on a criterion, this extension is compensatory too, and will not eliminate anything below a threshold.
Mistakes Specific to This Extension
Value-space violation. In every cell, the sum of support, abstention and rejection must not exceed 1. This check must be made before the average solution is built.
Forgetting to complete a cost criterion. If support and rejection are left unswapped in a cost-direction criterion, the alternative with high support on that criterion is wrongly counted as favourable.
Changing the score function midway through. The support-minus-rejection score must stay the same in every step. Using one function while building the average and a different one while computing the deviation makes the result inconsistent.
Defuzzifying first and then running crisp EDAS. Reducing the three degrees to a single number at the outset and then applying the crisp method is not this extension. The abstention and opposing-vote information is erased in the first step.
Inventing a triple from a single proportion. Saying "there is 60 per cent support, so 40 per cent is opposed" sets the abstention share to zero. As the Picture Fuzzy data-type card explains, every degree must be counted separately.
The governing principle is this:
Picture fuzzy EDAS exists to carry a board's or a survey's abstention share through to the average solution. Any application that invents a degree or crispens the input from the outset erases the method's one contribution.
Cases
The first case is an illustrative example; it is a small table DecisionMind has built for validation purposes, not taken from a page in a paper. This choice is deliberate: the application in Kamber (2026), on which the manifest rests, involves six alternatives, six criteria and a separate chain of weighting methods; this card uses only a small table showing PIF-EDAS's own steps (F1 through F7). The second case is an illustrative fiction.
1. Illustrative example: Three alternatives, three criteria (DecisionMind validation example)
Three alternatives are assessed on three criteria. C1 and C2 are "higher is better," C3 is "lower is better." Every cell carries a board's vote distribution on how much it supports that alternative on that criterion. The weights are 0.45 for C1, 0.30 for C2 and 0.25 for C3.
| Alternative | C1 | C2 | C3 (lower is better) |
|---|---|---|---|
| A1 | (0.70; 0.20; 0.05) | (0.50; 0.30; 0.10) | (0.30; 0.20; 0.40) |
| A2 | (0.60; 0.10; 0.20) | (0.40; 0.30; 0.20) | (0.20; 0.30; 0.50) |
| A3 | (0.50; 0.20; 0.20) | (0.60; 0.20; 0.10) | (0.40; 0.20; 0.30) |
| Direction | higher is better | higher is better | lower is better |
| Weight | 0.45 | 0.30 | 0.25 |
The method first completes C3, then builds the picture fuzzy average solution across the three criteria. It compares every alternative's score with the average's score, sums the weighted positive and negative deviations, and combines them into a single assessment score.
| Alternative | Assessment score | Rank |
|---|---|---|
| A2 | 0.8269 | 1 |
| A1 | 0.6907 | 2 |
| A3 | 0.1204 | 3 |
The result reads as follows. A2 falls below the average on C1, the heaviest criterion, but sits markedly in favour of the average on C3, where it is the cheapest alternative; these two criteria's combined weight is 0.70 and carries A2 into the lead. A3, meanwhile, stays against the average on both C1 and C3, and ends up last.
The board's hesitation is this: if C1's weight is raised from 0.45 to 0.70, C2's is lowered from 0.30 to 0.10, and C3's from 0.25 to 0.20, A1 moves ahead and scores 0.8743; A2 stays right behind it at 0.8685. This means A2's first place is sensitive to the relative weight of C1 and C3.
In the report: "With the given weights, A2 is in the most advantageous position relative to the set's average (0.8269). If the weight of C1 is markedly increased, A1 moves ahead; the order is sensitive to this criterion's weight."
Source: DecisionMind PIF-EDAS manifest, validation example. The steps follow Kamber's (2026) picture fuzzy EDAS algorithm; the average solution and the deviation calculation have been independently recomputed by this card's author with the kernel, and confirmed to match the manifest's expected results exactly within a tolerance of 1e-9.
2. Aviation: Fleet selection among three aircraft procurement bids
An airline is to choose among three procurement bids (T1, T2, T3) for a narrow-body aircraft fleet. There are four criteria: confidence in fuel efficiency, confidence in delivery schedule, cabin comfort satisfaction, and ease of maintenance; all four are "higher is better." The engineering team votes on fuel efficiency, the supply-chain team votes on delivery schedule, a passenger-panel survey covers cabin comfort, and the technical team votes on ease of maintenance. The airline has given the highest weight to fuel efficiency: fuel 0.40, delivery 0.25, comfort 0.15, maintenance 0.20.
The method builds the average solution across the four criteria and compares every bid's score with this average. Suppose the result places T1 first (0.7138), T2 second (0.5000), and T3 third (0.4051). T1 sits markedly in favour of the average on fuel efficiency, and this criterion carries the highest weight.
The airline's hesitation is this: if confidence in delivery schedule's weight is raised from 0.25 to 0.50 and the other criteria's weights are lowered accordingly (fuel 0.20, comfort 0.15, maintenance 0.15), T2 moves ahead and scores 0.5411; T1 falls back to 0.2036. This is because T2 stands out as the strongest bid on delivery schedule.
In the report: "With the given weights, T1 is in the most advantageous position relative to the set's average (0.7138). If the weight of the delivery-schedule criterion is markedly increased, T2 moves ahead; the order is sensitive to this criterion's weight."
3. What Not to Do
If C3 had been marked "higher is better" in the illustrative example, the most expensive alternative would move onto the average's favourable side, and A2's advantage from low cost would be reversed. The second error is the board adding a fourth alternative after the analysis has finished; this changes the average solution and therefore all the scores. The third error is reporting A2's score of 0.8269 as "83 per cent suitable"; the score only compares these three alternatives against each other relative to the set's own average.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/pif-edas
Kamber, E. (2026). Yükseköğrenimde Yenilikçi Eğitim Teknolojilerinin Seçimi: Resim Bulanık EDAS ve Best Worst Yöntemi ile Bir Uygulama. Alanya Akademik Bakış, 10(1), 142–160. DOI: 10.29023/alanyaakademik.1655523
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica, 26(3), 435–451. DOI: 10.15388/Informatica.2015.57
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets — A new concept for computational intelligence problems. 2013 Third World Congress on Information and Communication Technologies (WICT 2013), 1–6. DOI: 10.1109/WICT.2013.7113099
Cuong, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409–420. DOI: 10.15625/1813-9663/30/4/5032