topsis熵权法python代码
时间: 2024-06-16 19:07:07 浏览: 19
TOPSIS(Technique for Order of Preference by Similarity to Ideal Solution)是一种多属性决策分析方法,用于评估和排序一组备选方案。熵权法是一种确定指标权重的方法,它基于信息熵的概念。
以下是一个使用Python实现TOPSIS和熵权法的示例代码:
```python
import numpy as np
def topsis(data, weights, impacts):
# 数据归一化
normalized_data = data / np.sqrt(np.sum(data**2, axis=0))
# 加权归一化矩阵
weighted_normalized_data = normalized_data * weights
# 理想解和负理想解
ideal_solution = np.zeros(data.shape)
negative_ideal_solution = np.zeros(data.shape)
for i in range(data.shape):
if impacts[i] == '+':
ideal_solution[i] = np.max(weighted_normalized_data[:, i])
negative_ideal_solution[i] = np.min(weighted_normalized_data[:, i])
elif impacts[i] == '-':
ideal_solution[i] = np.min(weighted_normalized_data[:, i])
negative_ideal_solution[i] = np.max(weighted_normalized_data[:, i])
# 计算每个备选方案与理想解和负理想解的距离
positive_distances = np.sqrt(np.sum((weighted_normalized_data - ideal_solution)**2, axis=1))
negative_distances = np.sqrt(np.sum((weighted_normalized_data - negative_ideal_solution)**2, axis=1))
# 计算综合评价指数
performance_scores = negative_distances / (positive_distances + negative_distances)
# 返回排序结果
rankings = np.argsort(performance_scores)[::-1]
return rankings
# 示例数据
data = np.array([[3, 4, 5], [2, 6, 8], [1, 3, 7], [4, 5, 6]])
weights = np.array([0.4, 0.3, 0.3])
impacts = ['+', '+', '+']
# 调用TOPSIS函数
rankings = topsis(data, weights, impacts)
print(rankings)
```
上述代码中,`data`是一个二维数组,表示备选方案的各个指标值;`weights`是一个一维数组,表示各个指标的权重;`impacts`是一个一维数组,表示各个指标的影响方向(正向指标为'+',负向指标为'-')。函数返回一个排序结果,表示备选方案的优劣顺序。