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EDAS as a visible comparison with the average solution
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Full chapter index · Independent practice · Judgement subject guide
Evaluation based on Distance from Average Solution, or EDAS, ranks alternatives by how far each criterion value lies above or below that criterion’s average. Benefit and cost directions are handled explicitly. Weighted positive and negative distances are normalised, then combined into an appraisal score. The calculation is compact, but the judgement is not automatic: criteria, weights, scales, feasibility and the option set remain human responsibilities.
This guide reconstructs a small fictional decision, checks every transformation, and shows why a ranking can change when weights, measurements or alternatives change. EDAS is treated as an auditable decision aid, not a machine for discovering the one true answer.
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Full chapter index
See the mechanism · Chapters 1–2
Build the worked model · Chapters 3–5
Test what changes · Chapters 6–8
Check evidence and limits · Chapters 9–10
Practise and continue · Chapters 11–12
Name the decision owner, alternatives, affected people, deadline and decision that will follow the ranking. Separate feasibility constraints from preferences. An unsafe or unaffordable option should not become acceptable merely because strengths on other criteria compensate for it.
Define each criterion in plain language, with unit, direction, measurement date and evidence owner. Avoid counting the same consequence twice under correlated labels. Keep raw values beside transformed values so readers can return to the evidence.
EDAS suits a finite set of alternatives evaluated on conflicting criteria. It does not create missing objectives, settle ethical disputes about weights, or model causal consequences. Those tasks must be completed or bounded first.
Evidence check: for Frame the decision before choosing the method, preserve the observation before the interpretation. Record decision owner, alternatives and constraints. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
For each criterion, calculate the arithmetic mean across the included alternatives. This vector is the average solution. It is not an ideal, target, benchmark or policy standard. It changes when the option set changes.
That dependence matters. Adding a dominated or unrealistic option can shift the average and alter distances among existing alternatives. Therefore freeze the eligible option set before primary calculation and treat option-set changes as sensitivity analyses.
The average also inherits the criterion’s scale and outliers. A single extreme cost can move the cost average substantially. Inspect distributions and units before trusting the reference point. EDAS arithmetic cannot rescue a poorly defined criterion.
Evidence check: for Understand the average solution, preserve the observation before the interpretation. Record criteria, directions, units and weights. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 3 OF 12 · Build the worked model
3. Compute direction-aware positive and negative distances
For a benefit criterion, positive distance from average is max(0, value minus average) divided by the absolute average. Negative distance is max(0, average minus value) divided by the absolute average. For a cost criterion, reverse the desirable direction: a value below average creates positive distance, while a value above average creates negative distance.
Using the absolute average avoids a sign flip, but a zero or near-zero average makes the ratio undefined or unstable. In such cases, reconsider the scale, transform the criterion with substantive justification, or use another method. Never add a tiny arbitrary constant without reporting its effect.
The max operation means each value contributes to either positive or negative distance for a criterion, not both. Preserve enough decimals for reconstruction, and round only displayed outputs.
Evidence check: for Compute direction-aware positive and negative distances, preserve the observation before the interpretation. Record the average solution for every criterion. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Suppose a school service compares options A, B and C on reliability, access and weekly cost. Reliability and access are benefits; cost is a cost. Weights are 0.40, 0.35 and 0.25 and sum to one. The table contains fictional teaching values, not a recommendation about a real service.
The criterion averages are 83.0 for reliability, 77.0 for access and about 67.67 for cost. For option A, reliability 82 is below average, so its negative reliability distance is (83−82)/83 ≈ 0.0120. Access 74 is below average, giving negative distance (77−74)/77 ≈ 0.0390. Cost 66 is desirable because it is below the cost average, giving positive distance (67.67−66)/67.67 ≈ 0.0246.
Repeat each calculation for B and C with the direction rule visible. A spreadsheet should include raw value, average, direction, numerator, denominator and result. This prevents a common error: treating low cost as a negative feature.
| Option | Reliability benefit | Access benefit | Weekly cost |
|---|---|---|---|
| A | 82 | 74 | 66 |
| B | 76 | 88 | 58 |
| C | 91 | 69 | 79 |
| Weight | 0.40 | 0.35 | 0.25 |
Evidence check: for Work a fictional three-option matrix, preserve the observation before the interpretation. Record every positive and negative distance term. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
For each alternative, multiply every positive distance by its criterion weight and sum to obtain the weighted positive-distance total. Do the same for negative distances. These totals preserve two ideas: advantage above average and disadvantage below average.
Audit the weights before use. They represent trade-offs over the stated criterion ranges, not abstract importance labels. If one criterion uses a narrow observed range and another a broad one, identical verbal weights may not express the intended swing. Elicit or validate weights against concrete changes.
Keep the positive and negative totals in the results. A final score alone hides whether an option wins through strong advantages, small disadvantages or both.
Evidence check: for Aggregate weighted distances, preserve the observation before the interpretation. Record weighted sums and normalisation bounds. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
The original EDAS procedure normalises positive totals by the largest positive total. Negative totals are converted so that the smallest disadvantage is best, commonly as one minus each negative total divided by the maximum negative total. The appraisal score is the average of these two normalised quantities.
Check edge cases. If every positive total is zero, the positive normalisation has a zero denominator. If every negative total is zero, the negative term does too. Define a documented rule or recognise that the data provide no discrimination on that component. Software should fail visibly rather than return not-a-number or silently treat all alternatives as perfect.
Reconstruct the highest and lowest scores independently. Confirm the final ranking uses descending appraisal score and that ties are preserved rather than broken by row order.
Evidence check: for Normalise and calculate the appraisal score, preserve the observation before the interpretation. Record appraisal score reconstruction. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 7 OF 12 · Test what changes
7. Interpret the ranking without erasing the pattern
An appraisal score is relative to this matrix, weight vector and option set. It is not a probability of success or a percentage of the ideal. Report the raw matrix, averages, positive and negative totals, normalised terms and score together.
Examine profile differences. One option may have the best positive distance but a serious cost disadvantage. Another may be consistently near average with few weaknesses. Decision owners may care about that pattern even when the final ranking is clear.
If a non-compensable threshold exists, apply it before or alongside EDAS. For example, minimum reliability can be a feasibility rule. Do not let excellent access offset a breach that policy treats as unacceptable.
Evidence check: for Interpret the ranking without erasing the pattern, preserve the observation before the interpretation. Record zero-average and sign edge cases. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 8 OF 12 · Test what changes
8. Compare EDAS with neighbouring methods carefully
EDAS uses the average solution, while TOPSIS compares distances to ideal and anti-ideal points. MOORA’s ratio system aggregates direction-aware normalised criteria, and COPRAS and WASPAS use other proportional or sum-product structures. Different methods can rank the same matrix differently because they encode different comparison logic.
Use MOORA and MULTIMOORA, COPRAS, and WASPAS as neighbouring reading routes, not as interchangeable buttons.
Method comparison is useful when the decision is sensitive to reference-point philosophy. It becomes method shopping if analysts report only the technique that produced a preferred winner. Pre-specify the primary model and explain why it fits the judgement.
Evidence check: for Compare EDAS with neighbouring methods carefully, preserve the observation before the interpretation. Record rank ties and option-set dependence. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 9 OF 12 · Check evidence and limits
9. Test weights, measurements, scales and the option set
Run weight scenarios that represent plausible stakeholder trade-offs and preserve a sum of one. Perturb uncertain measurements within defensible intervals. Add or remove an option only when the eligibility question is itself relevant, and observe whether the average reference shifts existing ranks.
Check scale transformations. Changing dollars to cents should not matter because it is a positive linear rescaling, but shifting a scale by an arbitrary constant can change relative distances from the mean. Ordinal ratings should not be treated as interval measurements without justification.
Summarise rank stability, score ranges and pairwise reversals. A stable winner across tested scenarios supports a stronger recommendation. An unstable top pair calls for more evidence, revised criteria or a conditional recommendation.
| Test | Changed | Held fixed | Question |
|---|---|---|---|
| Weight scenario | Trade-offs | Raw matrix | Preference sensitivity? |
| Uncertain value | One interval | Criteria and options | Measurement sensitivity? |
| Dominated option | Option set | Old rows and weights | Average-reference shift? |
| Hard constraint | Feasibility rule | EDAS arithmetic | Compensation limit? |
Evidence check: for Test weights, measurements, scales and the option set, preserve the observation before the interpretation. Record weight, interval and scaling sensitivity. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
EDAS is compensatory unless constraints or vetoes are added. It assumes criterion values and weights are commensurable after its relative-distance transformation. It does not model interaction automatically, and correlated criteria can double-count effects.
The average reference is endogenous to alternatives, so rank reversal can occur when the option set changes. Outliers and near-zero means can distort distances. Uncertain or disputed data require explicit ranges, scenarios or other methods rather than false precision.
A technically correct spreadsheet can still support an illegitimate decision if affected people had no voice, criteria omit important harms, or weights are unexplained. Mathematical transparency is necessary but not sufficient for good judgement.
Evidence check: for Know the method’s limits, preserve the observation before the interpretation. Record compensation and governance limits. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 11 OF 12 · Practise and continue
11. Practise transfer with a dominated option and a hard threshold
Return to the fictional matrix. Add option D with lower reliability and access and higher cost than every existing option. It is dominated and should not be chosen, yet its values move every criterion average. Recalculate A, B and C. If their order changes, explain option-set dependence rather than treating the new rank as new evidence about them.
Then remove D and impose reliability of at least 80 as a hard constraint. Option B becomes infeasible despite potential strengths elsewhere. Compare that decision with an unconstrained EDAS ranking. State who authorised the threshold and what evidence supports it.
Finally increase the cost weight and reduce the access weight. Identify the weight at which the leading pair reverses. That threshold is more informative than saying the model is “sensitive.”
Evidence check: for Practise transfer with a dominated option and a hard threshold, preserve the observation before the interpretation. Record the added dominated option changed context. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 12 OF 12 · Practise and continue
12. Continue through the primary source and Judgement route
Read the original open-access paper, Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution, and its full PDF. Keshavarz Ghorabaee, Zavadskas, Olfat and Turskis introduced EDAS in 2015. The paper explains the algorithm in an inventory-classification application; using the method elsewhere still requires a defensible decision model.
Return to The Gold Standard of Judgement for the wider route. Preserve a decision record with alternatives, exclusions, raw evidence, criterion directions, units, averages, formulas, unrounded distances, weights, constraints, sensitivity scenarios, software version, results and reasons.
The gold standard is not merely reproducing the score. It is making the assumptions visible enough that another reader can change one of them, obtain the expected new result, and understand why the recommendation did or did not survive.
Evidence check: for Continue through the primary source and Judgement route, preserve the observation before the interpretation. Record the narrowest defensible EDAS recommendation. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.