python利用熵权TOPSIS法对IEEE30节点系统的度中心性、接近中心性、pagerank算法、失同步扩散时间倒数和临界同步耦合强度建立多指标综合判别方法，对节点重要度排序，详细写明每一步的代码

首先，我们需要导入需要的库。

import numpy as np
import pandas as pd
from sklearn.preprocessing import minmax_scale

接下来，我们需要读入IEEE30节点系统的度中心性、接近中心性、pagerank算法、失同步扩散时间倒数和临界同步耦合强度等指标数据。

data = pd.read_csv('data.csv')

然后，我们需要对数据进行标准化处理。

data_std = minmax_scale(data)

接下来，我们需要求出每个指标的权重，可以使用熵权TOPSIS法。

def entropy_weight(data):
    m, n = data.shape
    # 求解熵值
    entropy = np.zeros(n)
    for i in range(n):
        p = data[:, i] / data[:, i].sum()
        entropy[i] = -np.dot(p, np.log(p))
    # 求解权重
    weight = (1 - entropy) / (n - entropy.sum())
    return weight

weight = entropy_weight(data_std)

然后，我们需要对数据进行加权处理。

data_weighted = data_std * weight

接下来，我们需要将数据进行正向化处理。

def positive_ideal(data_weighted):
    return np.max(data_weighted, axis=0)

def negative_ideal(data_weighted):
    return np.min(data_weighted, axis=0)

z_positive = positive_ideal(data_weighted)
z_negative = negative_ideal(data_weighted)

data_positive = (data_weighted - z_negative) / (z_positive - z_negative)

然后，我们需要计算每个节点的综合得分。

def topsis_score(data_positive, weight):
    m, n = data_positive.shape
    # 求解距离
    distance_positive = np.zeros(m)
    distance_negative = np.zeros(m)
    for i in range(m):
        distance_positive[i] = np.sqrt(np.sum((data_positive[i, :] - weight) ** 2))
        distance_negative[i] = np.sqrt(np.sum((data_positive[i, :] - (1 - weight)) ** 2))
    # 求解综合得分
    score = distance_negative / (distance_positive + distance_negative)
    return score

score = topsis_score(data_positive, weight)

最后，我们可以将节点按照得分从高到低进行排序。

node_ranking = np.argsort(-score)

完整代码如下：

import numpy as np
import pandas as pd
from sklearn.preprocessing import minmax_scale

data = pd.read_csv('data.csv')
data_std = minmax_scale(data)

def entropy_weight(data):
    m, n = data.shape
    # 求解熵值
    entropy = np.zeros(n)
    for i in range(n):
        p = data[:, i] / data[:, i].sum()
        entropy[i] = -np.dot(p, np.log(p))
    # 求解权重
    weight = (1 - entropy) / (n - entropy.sum())
    return weight

weight = entropy_weight(data_std)
data_weighted = data_std * weight

def positive_ideal(data_weighted):
    return np.max(data_weighted, axis=0)

def negative_ideal(data_weighted):
    return np.min(data_weighted, axis=0)

z_positive = positive_ideal(data_weighted)
z_negative = negative_ideal(data_weighted)

data_positive = (data_weighted - z_negative) / (z_positive - z_negative)

def topsis_score(data_positive, weight):
    m, n = data_positive.shape
    # 求解距离
    distance_positive = np.zeros(m)
    distance_negative = np.zeros(m)
    for i in range(m):
        distance_positive[i] = np.sqrt(np.sum((data_positive[i, :] - weight) ** 2))
        distance_negative[i] = np.sqrt(np.sum((data_positive[i, :] - (1 - weight)) ** 2))
    # 求解综合得分
    score = distance_negative / (distance_positive + distance_negative)
    return score

score = topsis_score(data_positive, weight)
node_ranking = np.argsort(-score)