Extension card · Picture
Picture fuzzy CIMAS-ARTASI (Kara et al., 2024)
This hybrid method carries the criterion weights produced by picture fuzzy CIMAS directly into picture fuzzy ARTASI's ranking step. Two picture fuzzy stages run one after the other: first a weighting, then, using these weights, a ranking of alternatives.
Base method
CIMAS →
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.
Cells. This extension has two separate picture fuzzy tables. The first (Stage 1, CIMAS) holds the (μ, η, ν) triples the experts give to criterion importance and criterion scores; it is exactly the form described on the Picture fuzzy CIMAS card. The second (Stage 2, ARTASI) is a separate (μ, η, ν) table showing the alternatives' performance on each criterion. When there is more than one expert, this table is first merged into a single table with the picture fuzzy weighted average (PFWA) operator.
Scale equalisation. The criterion weights produced by Stage 1 (the final step of picture fuzzy CIMAS) become the direct input to Stage 2. In Stage 2, every alternative-criterion cell is first reduced to a crisp score with the same formula, Sc = (μ + (1−η) + (1−ν)) / 3. It is then rescaled, on a fixed scale, into ARTASI's own adaptive interval, that is, the upper-lower bound derived from the column's own magnitude.
Distance, score and combination. ARTASI's own logic, that is, computing the ideal and anti-ideal benefit, summing the two and combining them with a balance term, runs here unchanged. The only difference is that, whereas crisp ARTASI takes the criterion weights from outside, here they come from Stage 1's picture fuzzy CIMAS calculation.
Result and defuzzification. The output, as in crisp ARTASI, is a single K score for every alternative and a ranking based on this score. The picture fuzziness, in both the weights and the alternative scores, is reduced to the Sc score at the start of the chain; the K score itself is crisp.
DecisionMind runs the two stages in this extension sequentially and independently: the weights produced by Stage 1 are fixed first, and Stage 2 then runs with these weights. ARTASI's internal balance parameter (ψ=0.5) and its standardisation bounds are held at their default values.
How to Read the Output
The K score, as in crisp ARTASI, is only a ranking within this set of alternatives; it is not a percentage and cannot be compared with a different analysis.
The difference is here: this ranking is the product of two separate picture fuzzy calculations. The final order depends both on the alternatives' own performance judgements and on which expert panel the criterion weights came from. A fragility in the weight calculation (Stage 1), such as a single expert's excessive self-confidence, leaks directly into Stage 2's ranking.
Thus instead of writing:
"This ranking reflects the alternatives' performance directly"
the report should read:
"This ranking reflects both the alternatives' performance and the expert panel behind the criterion weights; a fragility in the weight calculation is carried directly into the ranking"
When to Prefer This over the Base Method
Use this hybrid when both the criterion weight and the alternative performance come with the same kind of uncertainty, in the form of a picture fuzzy panel or vote. It particularly suits situations where you want a single end-to-end flow rather than managing these two stages separately. If you already have the weights, whether from another method or supplied directly, it is enough to use picture fuzzy ARTASI on its own; rerunning the CIMAS stage is needless complexity. Conversely, if you only want the weight and have no need for a ranking of alternatives, it is enough to stop at the Picture fuzzy CIMAS card without ever moving on to the ranking stage.
Mistakes Specific to This Extension
Skipping the reliability check (RI) in Stage 1. Unreliable expert assessments then leak into Stage 2 unchecked and go unnoticed in the ranking.
Blurring the qualitative/quantitative criterion distinction against the source paper's rule. The picture fuzzy triple is used only for qualitative, that is, unmeasurable, criteria; measured quantitative criteria should stay on their own scale.
Running the two stages with different expert panels without stating this in the report. Whether Stage 1 and Stage 2 run with the same panel or with clearly different ones changes how the result should be read.
Treating the ranking as a property of Stage 2 (ARTASI) alone. A small change in Stage 1 (CIMAS) can reverse the ranking; this is shown in detail in Case 1.
The governing principle is this:
This hybrid runs picture fuzzy weighting (CIMAS) and picture fuzzy ranking (ARTASI) one after the other. A fragility in the weighting stage is carried directly into the ranking stage; the report must assess the two together.
Cases
The first case is DecisionMind's validation example. The numerical application in Kara and colleagues' (2024) paper, across eight sites × twelve criteria × eight experts, could not be accessed during the build. DecisionMind has therefore used, for Stage 1, the same synthetic three-experts × three-criteria table as on the [picture fuzzy CIMAS card](pif-cimas.md), and, for Stage 2, an additional table of three alternatives. The second case is an illustrative fiction.
1. Illustrative example (DecisionMind's validation example): Weighted ranking of three alternatives
In Stage 1, the same three experts (E1, E2, E3) weight the same three criteria (C1, C2, C3) with the table on the Picture fuzzy CIMAS card, producing the weights C1=0.5071, C2=0.4786, C3=0.0143. In Stage 2, three alternatives (A1, A2, A3) are scored on the same three criteria with a picture fuzzy assessment (all criteria are benefit criteria):
| Alternative | C1 | C2 | C3 |
|---|---|---|---|
| A1 | (0.70; 0.10; 0.10) | (0.60; 0.20; 0.10) | (0.50; 0.20; 0.20) |
| A2 | (0.50; 0.20; 0.20) | (0.70; 0.10; 0.10) | (0.60; 0.20; 0.10) |
| A3 | (0.60; 0.20; 0.10) | (0.50; 0.20; 0.20) | (0.70; 0.10; 0.10) |
The method reduces every cell to the Sc score, scales it into ARTASI's adaptive interval, and sums the ideal and anti-ideal benefit using Stage 1's weights (C1=0.5071, C2=0.4786, C3=0.0143).
| Alternative | K score | Rank |
|---|---|---|
| A1 | 18,762.6 | 1 |
| A2 | 17,453.3 | 2 |
| A3 | 16,465.4 | 3 |
The result reads as follows: A1 comes out ahead because it holds the best score on C1, the criterion carrying the highest weight. Since C3's weight is close to zero (1.4 per cent), differences on this criterion have almost no effect on the ranking.
The team's hesitation: in Stage 1, as shown in the sensitivity scenario on the Picture fuzzy CIMAS card, if E1 had given a more moderate importance statement, the weights would turn into C1≈0.159, C2≈0.508, C3≈0.333. When Stage 2 is rerun with these new weights, the ranking reverses. A2 rises to first place (K≈18,394), A1 falls to second (K≈17,146), A3 stays third (K≈17,118); the gap between A1 and A3, meanwhile, nearly closes. This result has been verified with an independent Python calculation.
In the report: "With the current expert panel, A1 receives the highest K score (18,762.6), giving the order A1 > A2 > A3. This ranking is, however, sensitive to Stage 1's expert weighting: had E1 stated their own importance more moderately, the ranking would turn into A2 > A1 > A3, and the gap between A1 and A3 would nearly close."
Source: DecisionMind's picture fuzzy CIMAS-ARTASI validation example. It is faithful to the two-stage step order published in §2.2 by Kara, Yalçın, Kaygısız, Simić, Örnek and Pamučar (2024). This table is synthetic because the paper's own case study (website performance analysis, human resource management) could not be accessed during the build (see the approval notes). The K scores and the sensitivity scenario have been verified with an independent Python calculation.
2. Sports: Site selection for a new sports complex
A local government's sports directorate is to choose one of three site options (A1, A2, A3) for building a new sports complex. First, an expert panel (a civil engineer, an architect, a representative of the sports federation) weights the criteria of accessibility, ground suitability and environmental impact in picture fuzzy form. The three sites are then scored on the same three criteria in picture fuzzy form and ranked with these weights.
The method first computes the panel's criterion weights with CIMAS, then computes the ranking of sites with ARTASI. Suppose ground suitability receives the highest weight, and the site with the best score on this criterion comes out first.
The directorate's hesitation: one panel member (the architect) has stated a markedly higher importance for their own professional experience than the others. Without removing this member from the panel and recalculating the weights, there is no way to know whether ground suitability really is the most decisive criterion, or whether this single member's weight is driving the result.
In the report: "Ground suitability received the highest weight, and the site with the best score on this criterion came out ahead; how far this result depends on the panel's single most heavily weighted member should be tested separately."
3. What Not to Do
The first error is skipping the Stage 1 weight calculation, treating the criteria as equally important "by eye," and moving straight to Stage 2; this bypasses the hybrid's weighting contribution entirely. The second error is assuming that the illustrative example's ranking (A1 > A2 > A3) is a result of Stage 2 alone, and never testing the weight fragility in Stage 1; as shown, a single expert's importance statement can reverse the order. The third error is reading a K score, such as 18,762.6, as a percentage or a confidence score, and comparing it with another analysis's K score.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/pif-cimas-artasi
Kara, K., Yalçın, G. C., Kaygısız, E. G., Simić, V., Örnek, A. Ş., & Pamučar, D. (2024). A picture fuzzy CIMAS-ARTASI model for website performance analysis in human resource management. Applied Soft Computing, 162, 111826. DOI: 10.1016/j.asoc.2024.111826
Pamučar, D., Simić, V., Görçün, Ö. F., & Küçükönder, H. (2024). Selection of the best Big Data platform using COBRAC-ARTASI methodology with adaptive standardized intervals. Expert Systems with Applications, 239, 122312. DOI: 10.1016/j.eswa.2023.122312
Bošković, S., Jovčić, S., Simić, V., Švadlenka, L., Dobrodolac, M., & Bacanin, N. (2025). A new criteria importance assessment (CIMAS) method in multi-criteria group decision-making: Criteria evaluation for supplier selection. Facta Universitatis, Series: Mechanical Engineering, 23(2), 335–349. DOI: 10.22190/FUME230730050B
Cường, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409–420. DOI: 10.15625/1813-9663/30/4/5032