[数学建模]熵值法

计算指标权重的经典算法之一，用来判断某个指标的离散程度。离散程度越大，即信息量越大，不确定性就越小，熵也就越小；信息量越小，不确定性越大，熵也越大。根据熵的特性，通过计算熵值来判断一个事件的随机性及无序程度，也可以用熵值来判断某个指标的离散程度，指标的离散程度越大，该指标对综合评价的影响越大.

python代码

import pandas as pd
import numpy as np
from numpy import array

# 读取数据
doctor = pd.read_csv(r'D:\WorkSpace\PythonWork\Python学习\数据挖掘Baseline\熵权法实例.csv')
index = doctor['科室']
doctor = doctor.drop(['科室'],axis = 1)

#定义熵值法函数
def cal_weight(x):
    '''熵值法计算变量的权重'''
    # 标准化
    x = x.apply(lambda x: ((x - np.min(x)) / (np.max(x) - np.min(x))))
 
    # 求k
    rows = x.index.size  # 行
    cols = x.columns.size  # 列
    k = 1.0 / math.log(rows)
 
    lnf = [[None] * cols for i in range(rows)]
 
    # 矩阵计算--
    # 信息熵
    # p=array(p)
    x = array(x)
    lnf = [[None] * cols for i in range(rows)]
    lnf = array(lnf)
    for i in range(0, rows):
        for j in range(0, cols):
            if x[i][j] == 0:
                lnfij = 0.0
            else:
                p = x[i][j] / x.sum(axis=0)[j]
                lnfij = math.log(p) * p * (-k)
            lnf[i][j] = lnfij
    lnf = pd.DataFrame(lnf)
    E = lnf
 
    # 计算冗余度
    d = 1 - E.sum(axis=0)
    # 计算各指标的权重
    w = [[None] * 1 for i in range(cols)]
    for j in range(0, cols):
        wj = d[j] / sum(d)
        w[j] = wj
        # 计算各样本的综合得分,用最原始的数据
    
    w = pd.DataFrame(w)
    w.columns = ['weight']
    w.index = doctor.columns
    return w

w = cal_weight(doctor)  # 调用cal_weight
print(w)
print('运行完成!')

计算得分

array1 = np.array(doctor)
array2 = np.array(w)
score = array1.dot(array2)
score = pd.DataFrame(score)
score.columns = ['score']
score.index = index
print(score)