Method and assumptions
EDAS compares alternatives with each criterion’s arithmetic average. Above-average benefit or below-average cost produces positive distance. Positive and negative distances are weighted separately, then scaled by the largest totals in the current set. Higher AS is preferred.
This tool requires strictly positive ratio-scale data to preserve meaningful division by the average. It does not add an epsilon to zero or negative observations. If max SP=0, NSP=0; if max SN=0, NSN=1. If both vanish, every AS is 0.5 with tied rank. This explicit implementation convention is not a universal methodological result.
AVⱼ = Σᵢ xᵢⱼ / m
PDAᵢⱼ = max(0, xᵢⱼ − AVⱼ)/AVⱼ; NDAᵢⱼ = max(0, AVⱼ − xᵢⱼ)/AVⱼ [benefit / fayda]
Cost / maliyet: PDA ve NDA / PDA and NDA exchange numerators.
SPᵢ = Σ wⱼPDAᵢⱼ; SNᵢ = Σ wⱼNDAᵢⱼ
NSPᵢ = SPᵢ / max SP; NSNᵢ = 1 − SNᵢ / max SN
ASᵢ = (NSPᵢ + NSNᵢ)/2
i indexes alternatives, j criteria, m is the alternative count, x the raw value, a an entered weight and w its sum-to-one normalization. Higher scores are preferred. A 10⁻¹² score tolerance identifies tied ranks; ties are not arbitrarily converted into a winner.
Worked example
Invented maintenance-program comparison, not measured vessel data: cost in thousand EUR; quality and support are illustrative scores. Smaller cost and larger other scores are preferred. They are assumed cardinal for this exercise.
| Cost | Quality | Support | |
|---|---|---|---|
| A | 100 | 80 | 6 |
| B | 120 | 90 | 8 |
| C | 90 | 70 | 5 |
A: AV = (103.333333, 80, 6.333333); PDA = (0.0322581, 0, 0); NDA = (0, 0, 0.0526316); AS = 0.49063822
| Rank | Alternative | Score |
|---|---|---|
| 1 | B | 0.66530882 |
| 2 | A | 0.49063822 |
| 3 | C | 0.23559043 |
Bar length shows absolute magnitude; the number retains its sign. Scores from different methods are not on a common scale.
| Criterion | Weight |
|---|---|
| Cost | 0.4 |
| Quality | 0.35 |
| Support | 0.25 |
| Cost | Quality | Support | |
|---|---|---|---|
| AV | 103.33333 | 80 | 6.3333333 |
| Cost | Quality | Support | |
|---|---|---|---|
| A | 0.032258065 | 0 | 0 |
| B | 0 | 0.125 | 0.26315789 |
| C | 0.12903226 | 0 | 0 |
| Cost | Quality | Support | |
|---|---|---|---|
| A | 0 | 0 | 0.052631579 |
| B | 0.16129032 | 0 | 0 |
| C | 0 | 0.125 | 0.21052632 |
| Alternative | SP | SN | NSP | NSN | AS |
|---|---|---|---|---|---|
| A | 0.012903226 | 0.013157895 | 0.11779521 | 0.86348123 | 0.49063822 |
| B | 0.10953947 | 0.064516129 | 1 | 0.33061764 | 0.66530882 |
| C | 0.051612903 | 0.096381579 | 0.47118086 | 0 | 0.23559043 |
One-way weight sensitivity
The first weight is varied while the ratios of the remaining weights are preserved. These are sampled scenarios, not a probability, confidence interval or proof of robustness. If all remaining weights are zero, the scan is undefined.
| First criterion weight | A | B | C | Leading alternatives |
|---|---|---|---|---|
| 0 | 0.43174061 | 1 | 0 | B |
| 0.1 | 0.44155688 | 0.94421814 | 0.039265072 | B |
| 0.25 | 0.46118942 | 0.83265441 | 0.11779521 | B |
| 0.4 | 0.49063822 | 0.66530882 | 0.23559043 | B |
| 0.5 | 0.52036395 | 0.5 | 0.35541415 | A |
| 0.75 | 0.60233918 | 0.23581414 | 0.8340095 | C |
| 0.9 | 0.61744639 | 0.078604715 | 0.94466983 | C |
| 1 | 0.625 | 0 | 1 | C |
Limits and interpretation
The result depends on the preference model and supplied alternative set; it does not prove a uniquely correct decision. Justify weights and criterion directions, avoid double counting and examine sensitivity. Measurement uncertainty is not modeled here. Do not sum scores across methods into a new truth score. Qualified people must evaluate safety and regulatory constraints before ranking.