a5c-ai AHP Calculator
Overview
The AHP Calculator skill implements the Analytic Hierarchy Process methodology for multi-criteria decision analysis. It enables systematic evaluation of alternatives through pairwise comparisons, consistency validation, and weight derivation, supporting both individual and group decision-making scenarios.
Capabilities
- Pairwise comparison matrix creation
- Eigenvalue-based weight calculation
- Consistency ratio computation
- Inconsistency identification and correction guidance
- Group AHP aggregation (AIJ/AIP methods)
- Sensitivity analysis on weights
- AHP hierarchy visualization
- Report generation
Used By Processes
- Multi-Criteria Decision Analysis (MCDA)
- Structured Decision Making Process
- Decision Quality Assessment
Usage
AHP Scale
The standard Saaty scale for pairwise comparisons:
- 1: Equal importance
- 3: Moderate importance
- 5: Strong importance
- 7: Very strong importance
- 9: Extreme importance
- 2, 4, 6, 8: Intermediate values
Hierarchy Definition
# Define AHP hierarchy
hierarchy = {
"goal": "Select Best Vendor",
"criteria": [
{
"name": "Cost",
"sub_criteria": ["Initial Cost", "Maintenance Cost"]
},
{
"name": "Quality",
"sub_criteria": ["Product Quality", "Service Quality"]
},
{
"name": "Delivery",
"sub_criteria": ["Lead Time", "Reliability"]
}
],
"alternatives": ["Vendor A", "Vendor B", "Vendor C"]
}
Pairwise Comparison Matrix
# Criteria comparison matrix
criteria_comparison = {
"Cost": {"Cost": 1, "Quality": 3, "Delivery": 5},
"Quality": {"Cost": 1/3, "Quality": 1, "Delivery": 3},
"Delivery": {"Cost": 1/5, "Quality": 1/3, "Delivery": 1}
}
Consistency Analysis
The skill calculates:
- Consistency Index (CI): (lambda_max - n) / (n - 1)
- Consistency Ratio (CR): CI / RI (Random Index)
- Acceptable threshold: CR < 0.10
Group Decision Making
Aggregation methods supported:
- AIJ (Aggregation of Individual Judgments): Geometric mean of individual comparisons
- AIP (Aggregation of Individual Priorities): Geometric mean of derived weights
Input Schema
{
"hierarchy": {
"goal": "string",
"criteria": ["object"],
"alternatives": ["string"]
},
"comparisons": {
"criteria": "matrix",
"sub_criteria": "object of matrices",
"alternatives": "object of matrices"
},
"options": {
"aggregation_method": "AIJ|AIP",
"consistency_threshold": "number",
"sensitivity_analysis": "boolean"
}
}
Output Schema
{
"weights": {
"criteria": "object",
"sub_criteria": "object",
"alternatives": "object"
},
"global_weights": "object",
"ranking": ["string"],
"consistency": {
"CR": "number",
"is_consistent": "boolean",
"inconsistent_comparisons": ["object"]
},
"sensitivity": {
"critical_criteria": ["string"],
"stability_intervals": "object"
}
}
Best Practices
- Limit criteria to 7-9 items per level (cognitive limit)
- Always check consistency ratio before proceeding
- Revisit inconsistent comparisons with stakeholders
- Use geometric mean for group aggregation
- Perform sensitivity analysis on close rankings
- Document rationale for each pairwise comparison
Correction Guidance
When CR > 0.10, the skill identifies:
- Most inconsistent judgments
- Suggested adjustment directions
- Impact of corrections on final weights
Integration Points
- Connects with Stakeholder Preference Elicitor for data collection
- Feeds into TOPSIS Ranker for hybrid analysis
- Supports Decision Visualization for hierarchy diagrams
- Integrates with Consistency Validator for quality assurance