topsis熵权法伪代码

Topsis (Technique for Order Preference by Similarity to Ideal Solution) 熵权法是一种决策分析工具，它结合了模糊集理论和灰色关联度评价方法。以下是使用熵权法进行TOPSIS算法的一个简单伪代码：

// 定义函数
def calculateEntropy(data, column):
    total = sum(data)
    prob = [d / total for d in data]
    entropy = -sum([p * math.log(p, 2) for p in prob])
    return entropy

def normalizeData(data):
    min_val = min(data)
    max_val = max(data)
    return [(d - min_val) / (max_val - min_val) for d in data]

def entropyWeighting(matrix, criteria):
    # 对每个评价指标计算信息熵
    entropies = [calculateEntropy(column, matrix[i]) for i, column in enumerate(matrix.T)]
    
    # 计算标准差作为熵权
    stds = [math.sqrt(sum([(ei - ei_mean)**2 for ei in row])) for ei_mean, row in zip(entropies, matrix.T)]
    weights = [1 / e if s > 0 else 0 for e, s in zip(entropies, stds)]  # 如果标准差为0，则赋予最大权重
    
    # 归一化权重
    weight_sum = sum(weights)
    normalized_weights = [w / weight_sum for w in weights]
    
    return normalized_weights

def topsisEntropy(matrix, ideal_solution, anti_ideal_solution, weights):
    normalized_matrix = [[row_i * w for row_i, w in zip(row, weights)] for row in matrix]
    
    # 计算距离向量
    distance_to_ideal = [sum((vector - ideal_solution) ** 2) for vector in normalized_matrix]
    distance_to_anti_ideal = [sum((vector - anti_ideal_solution) ** 2) for vector in normalized_matrix]
    
    # 最优解和最劣解排序
    best_alternatives = sorted(range(len(distance_to_ideal)), key=lambda x: distance_to_ideal[x], reverse=True)
    worst_alternatives = sorted(range(len(distance_to_ideal)), key=lambda x: distance_to_anti_ideal[x])

    # 返回最佳和次佳方案
    return best_alternatives[0], best_alternatives[1]

// 调用函数并处理数据
matrix_data = ...  // 评估矩阵
criteria = ...   // 权重向量或准则列
ideal_solution = ... // 理想解向量
anti_ideal_solution = ... // 反理想解向量

weights = entropyWeighting(matrix_data, criteria)
best, second_best = topsisEntropy(matrix_data, ideal_solution, anti_ideal_solution, weights)