Method and assumptions
This tool implements an alternative-set-dependent linear min–max scaling variant of SAW/WSM. Raw cost, time and scores are never added directly. Each column is mapped to 0–1 using its own extremes. A constant column receives r=0, with no redistribution of its weight. This convention adds no artificial discrimination.
The additive model is compensatory: a poor value on one criterion can be offset by another. Apply mandatory safety constraints before ranking; a large weight cannot replace a hard constraint. Weights should represent contributions over the stated worst-to-best ranges. AHP or entropy weights are not automatically valid trade-off coefficients.
rᵢⱼ = (xᵢⱼ − min xⱼ)/(max xⱼ − min xⱼ) [benefit / fayda]
rᵢⱼ = (max xⱼ − xᵢⱼ)/(max xⱼ − min xⱼ) [cost / maliyet]
wⱼ = aⱼ / Σ aₖ; Sᵢ = Σ wⱼ rᵢⱼ
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: 0.4 × (120−100)/30 + 0.35 × (80−70)/20 + 0.25 × (6−5)/3 = 0.525
| Rank | Alternative | Score |
|---|---|---|
| 1 | B | 0.6 |
| 2 | A | 0.525 |
| 3 | C | 0.4 |
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 | |
|---|---|---|---|
| min | 90 | 70 | 5 |
| max | 120 | 90 | 8 |
| Cost | Quality | Support | |
|---|---|---|---|
| A | 0.66666667 | 0.5 | 0.33333333 |
| B | 0 | 1 | 1 |
| C | 1 | 0 | 0 |
| Cost | Quality | Support | |
|---|---|---|---|
| A | 0.26666667 | 0.175 | 0.083333333 |
| B | 0 | 0.35 | 0.25 |
| C | 0.4 | 0 | 0 |
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 | 0.43055556 | 1 | 0 | B |
| 0.1 | 0.45416667 | 0.9 | 0.1 | B |
| 0.25 | 0.48958333 | 0.75 | 0.25 | B |
| 0.4 | 0.525 | 0.6 | 0.4 | B |
| 0.5 | 0.54861111 | 0.5 | 0.5 | A |
| 0.75 | 0.60763889 | 0.25 | 0.75 | C |
| 0.9 | 0.64305556 | 0.1 | 0.9 | C |
| 1 | 0.66666667 | 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.