Decision Science

Analytic Hierarchy Process

Design a pairwise-comparison questionnaire, collect expert judgements on the Saaty scale, and rank alternatives using transparent AHP calculations.

Browser-based calculation Questionnaire JSON workflow Consistency ratio check

Why use this tool?

Decision Supported

Use this tool when a decision has several criteria and several alternatives that need structured expert judgement.

What It Tells You

It estimates criterion weights, alternative scores under each criterion, overall ranking, and consistency ratios for the expert judgements.

Example Input

Define criteria such as cost, quality, risk, and implementation time, then compare alternatives pairwise under each criterion.

Sample Output Interpretation

The top-ranked alternative has the highest weighted score. High consistency ratios suggest the comparisons should be reviewed before acting.

1 Design Define the goal, criteria, and alternatives
2 Expert Survey Record pairwise judgements
3 Analysis Calculate weights and ranking

1. Questionnaire Design

Create the AHP decision structure before sending it to experts.

Sample template

Questionnaire design is created locally in your browser. Export the JSON file before sharing it with experts.

Project title Number of criteria Number of alternatives

2. Expert Survey

Import a questionnaire JSON, complete the pairwise comparisons, and export the expert response.

Survey answers are held in this browser session only. Export the completed response JSON before closing or refreshing the page.

Import questionnaire JSON

3. AHP Analysis

Load one or more completed expert response JSON files to calculate weights, consistency, and alternative ranking.

Import completed expert response JSON

4. Results and Interpretation

Review the calculated priority weights, consistency checks, and final ranking.

Criteria Weight Distribution

Alternative Ranking

Pairwise Comparison Calculations

Trace the calculation from the aggregated pairwise judgements through geometric-mean priorities and consistency checks. Select any matrix below to view its calculation.

Decision Matrix and Weighted Calculation

The final matrix combines each alternative's local priority under every criterion with the criterion weights.

Scenario Planning: Test Weight Sensitivity

Test whether the preferred alternative changes when one criterion receives more or less importance.

About Analytic Hierarchy Process

Analytic Hierarchy Process is a structured method for multi-criteria decision-making. It asks experts to compare criteria and alternatives in pairs, converts those judgements into priority weights, and combines the weights into an overall ranking.

Guidance

Define the decision goal, criteria, and alternatives in the questionnaire design section.
Export the blank questionnaire JSON and send it to the expert or decision-maker.
The expert imports the questionnaire, answers each pairwise question, and exports the completed response JSON.
Load one or more completed response files into the analysis section and calculate the ranking.
Review consistency ratios before using the ranking to support a decision.
Optionally turn on Scenario Planning after calculation to test whether changes in criterion importance alter the preferred alternative.

Methodology, Assumptions, and Limitations

Formula Logic

Notation
E = number of experts, n = number of compared elements, a_ij^(e) = expert e's judgement comparing element i with element j, w_i = priority weight

Reciprocal pairwise matrix
a_ji = 1 / a_ij, a_ii = 1

Multiple-expert aggregation
A_ij = (∏_e=1^E a_ij^(e))^1/E

Row geometric mean
GM_i = (∏_j=1ⁿ A_ij)^1/n

Normalised priority weight
w_i = GM_i / ∑_k=1ⁿ GM_k

Final alternative priority
S_a = ∑_i=1ⁿ w_i × p_ai, where p_ai is alternative a's local priority under criterion i

Sensitivity scenario
w′_k = s, w′_j = w_j × (1 - s) / (1 - w_k)

Consistency Ratio

Consistency vector
(Aw)_i / w_i

Principal value
λ_max = (1 / n) ∑_i=1ⁿ ((Aw)_i / w_i)

Consistency index
CI = (λ_max - n) / (n - 1)

Consistency ratio
CR = CI / RI

RI is Saaty's random index for a matrix of size n. A CR around 0.10 or lower is commonly used as review guidance, not proof that the judgement is objectively correct.

Saaty Scale

Ratings use 1 equal, 2 equal to moderate, 3 moderate, 4 moderate to strong, 5 strong, 6 strong to very strong, 7 very strong, 8 very strong to extreme, and 9 extreme preference.

Assumptions

Experts can make meaningful pairwise judgements, criteria are relevant to the decision, and alternatives are comparable under each criterion.

Limitations

AHP supports structured judgement but does not remove bias. Poorly defined criteria or inconsistent responses can produce misleading rankings.

FAQ

What is the Saaty scale?

It is a 1 to 9 judgement scale used for pairwise comparison. A value of 1 means equal importance or preference, while 9 means extreme importance or preference.

Can several experts answer the same questionnaire?

Yes. Send the same questionnaire JSON to each expert, then load multiple completed response files in the analysis section. The tool aggregates judgements using a geometric mean.

What does consistency ratio mean?

It checks whether the pairwise comparisons are reasonably coherent. A high consistency ratio means the expert should review the answers before the ranking is used.

Is my survey data uploaded?

No. This tool reads, calculates, and exports JSON files in the browser. No server upload is used by this static page.