The Analytic Hierarchy Process (AHP): Step 1 to the Perfect Decision Matrix for Better Decision Making

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Analytic Hierarchy Process (AHP) Decision Engine

AHP Consistency Ratio (CR) Calculator

Validate mathematical rigor, calculate principal eigenvalue (λ_max), priority vector weights (w_i), consistency index (CI), and consistency ratio (CR).

1 Define Decision Criteria

Add between 2 to 10 criteria for pairwise matrix evaluation.

2 Pairwise Comparisons (Saaty 1–9 Scale)

Adjust relative importance sliders. Center (0) denotes equal priority (1:1).

3 AHP Consistency Analysis

Evaluates transitivity logic: if Criterion A > B and B > C, then A should > C.

Principal Eigenvalue (λ_max) --

Consistency Index (CI) --

Random Index (RI) --

Consistency Ratio (CR) --

Calculated Priority Vector (w_i) Weights

Relative weighting allocated to each decision criterion.

AHP Mathematical Foundations

1. Pairwise Comparison Matrix (A)

For n criteria, an n × n pairwise matrix is built where each element a_ij represents the relative weight of criterion i over j, satisfying reciprocal symmetry: a_ji = 1 / a_ij and a_ii = 1.

2. Priority Vector / Row Averages (w_i)

Column-normalize matrix A and compute the arithmetic row mean to calculate normalized priority weights:

3. Principal Eigenvalue (λ_max)

Multiply original matrix A by priority vector w, divide row-wise by w_i, and take the average:

4. Consistency Index (CI) & Consistency Ratio (CR)

Quantifies random departure from exact transitivity:

Where RI is Thomas L. Saaty's empirical Random Index based on sample size n. Matrices with CR ≤ 10% (0.10) are considered consistently reliable for operational decision-making.

Action completed successfully!

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Updated: 06/10/20206 Changes made: AHP Consistency Analysis added. Radar chart added. Comparison Matrix and Normalized Matrix are added.