45 lines
1.5 KiB
Python
45 lines
1.5 KiB
Python
|
"""评价类题目的标准流程：无量纲化 → 赋权 → TOPSIS 排序 → 敏感性。
|
|||
|
|
|
|||
|
|
这是中文建模赛出现频率最高的题型之一。
|
|||
|
|
关键点（也是最容易翻车的地方）：**指标方向必须显式声明**。
|
|||
|
|
"""
|
|||
|
|
|
|||
|
|
from __future__ import annotations
|
|||
|
|
|
|||
|
|
import numpy as np
|
|||
|
|
|
|||
|
|
from mcm_toolkit.decision import entropy_weights, topsis
|
|||
|
|
from mcm_toolkit.solve import robustness_test
|
|||
|
|
|
|||
|
|
|
|||
|
|
def main() -> None:
|
|||
|
|
# 3 个城市 × 4 个指标
|
|||
|
|
# 人均GDP(效益) 空气PM2.5(成本) 绿化率(效益) 通勤时间(成本)
|
|||
|
|
X = np.array(
|
|||
|
|
[
|
|||
|
|
[120.0, 35.0, 42.0, 38.0],
|
|||
|
|
[95.0, 55.0, 36.0, 29.0],
|
|||
|
|
[140.0, 28.0, 45.0, 47.0],
|
|||
|
|
]
|
|||
|
|
)
|
|||
|
|
labels = ["城市A", "城市B", "城市C"]
|
|||
|
|
benefit = [0, 2] # 只有第 0、2 列是"越大越好"
|
|||
|
|
|
|||
|
|
# 1) 客观赋权
|
|||
|
|
w = entropy_weights(X, benefit_columns=benefit)
|
|||
|
|
print("熵权：", np.round(w.params["weights"], 4))
|
|||
|
|
|
|||
|
|
# 2) TOPSIS 排序
|
|||
|
|
result = topsis(X, weights=w.params["weights"], benefit_columns=benefit, labels=labels)
|
|||
|
|
print(result.data)
|
|||
|
|
|
|||
|
|
# 3) 鲁棒性：权重扰动 ±10% 后排名还稳不稳？（论文里必须回答这个问题）
|
|||
|
|
def model(**kw):
|
|||
|
|
return topsis(X, weights=kw["weights"], benefit_columns=benefit).data["rank"].tolist()
|
|||
|
|
|
|||
|
|
rob = robustness_test(model, params={"weights": w.params["weights"]}, perturbation=0.1, n_samples=500, random_state=0)
|
|||
|
|
print("排名稳定性：", rob.metrics)
|
|||
|
|
|
|||
|
|
|
|||
|
|
if __name__ == "__main__":
|
|||
|
|
main()
|