ahp-weighting · diff
v1.0.0 to v1.0.0
14 added, 13 removed. Audit A to A.
---
name: ahp-weighting
- description: 'SOP: 使用 AHP 层次分析法确定评分维度权重，输出权重向量'
+ description: 'SOP: Use the AHP (Analytic Hierarchy Process) to determine scoring-dimension weights, outputting a weight vector'
version: 1.0.0
category: hypothesis-formation
type: sop
campaign: gap-prioritization
- input: 维度列表（字符串数组）+ 可选的两两比较偏好矩阵
- output: AHPWeights — 权重向量、一致性比率（CR）及判断矩阵
+ input: List of dimensions (string array) + optional pairwise comparison preference matrix
+ output: AHPWeights — weight vector, consistency ratio (CR), and judgment matrix
dependencies:
skills:
- subagent-spawning
---
# AHP Weighting
- 使用 AHP 层次分析法确定评分维度权重，输出权重向量。
+ Use the AHP (Analytic Hierarchy Process) to determine scoring-dimension weights, outputting a weight vector.
## HARD-GATE
<HARD-GATE>
- - 输入维度数量必须在 [2, 9] 范围内（AHP 适用范围）
- - 输出权重向量各元素之和必须等于 1.0（允许 ±0.001 误差）
- - 一致性比率 CR 必须被计算并报告；若 CR > 0.1 必须标记警告
+ - The number of input dimensions must be in the range [2, 9] (AHP applicability range)
+ - The elements of the output weight vector must sum to 1.0 (±0.001 tolerance allowed)
+ - The consistency ratio CR must be computed and reported; if CR > 0.1 a warning must be flagged
</HARD-GATE>
## Pipeline
- 1. **前置检查**: 验证维度列表非空且数量在 [2, 9] 范围内
- 2. **维度列表确认**: 输出维度列表供调用方确认；若已提供比较矩阵则跳至步骤 4
- 3. **两两比较矩阵构建**: 对每对维度 (i, j) 赋予 Saaty 标度值（1-9）；矩阵满足 a[j][i] = 1/a[i][j]
- 4. **特征向量计算**: 对每列归一化后取行均值，得到优先级向量（权重）
- 5. **一致性比率检验**: 计算最大特征值 λ_max → 一致性指数 CI = (λ_max - n)/(n-1) → CR = CI/RI（查 Saaty RI 表）；CR < 0.1 为可接受
- 6. **输出**: 返回 AHPWeights 对象；若 CR > 0.1 附加修正建议
+ 1. **Precondition check**: verify the dimension list is non-empty and its count is in the range [2, 9]
+ 2. **Dimension list confirmation**: output the dimension list for the caller to confirm; if a comparison matrix is already provided, skip to step 4
+ 3. **Pairwise comparison matrix construction**: for each pair of dimensions (i, j) assign a Saaty scale value (1-9); the matrix must satisfy a[j][i] = 1/a[i][j]
+ 4. **Eigenvector computation**: normalize each column then take row means to obtain the priority vector (weights)
+ 5. **Consistency ratio check**: compute the largest eigenvalue λ_max → consistency index CI = (λ_max - n)/(n-1) → CR = CI/RI (look up the Saaty RI table); CR < 0.1 is acceptable
+ 6. **Output**: return the AHPWeights object; if CR > 0.1 attach revision suggestions
## Output Format
```json
{
"dimensions": ["importance", "feasibility", "novelty", "impact"],
"comparison_matrix": [[1, 3, 2, 2], [0.33, 1, 0.5, 0.5], [0.5, 2, 1, 1], [0.5, 2, 1, 1]],
"weights": { "importance": 0.40, "feasibility": 0.15, "novelty": 0.23, "impact": 0.22 },
"lambda_max": 4.02,
"ci": 0.007,
"ri": 0.90,
"cr": 0.008,
"cr_acceptable": true,
"warnings": [],
"revision_suggestions": []
}
```
+ </output>