### Topsis算法实现综合评价 #### Python代码示例 下面是一个基于Python的Topsis算法实现，用于进行综合评价： ```python import numpy as np import pandas as pd def normalize_data(data): """对数据标准化处理""" norm = data.apply(lambda x: (x ** 2).sum() ** 0.5, axis=0) normalized_df = data.div(norm) return normalized_df def calculate_weighted_normalized_matrix(normalized_df, weights): """计算加权规范化矩阵""" weighted_normalized_df = normalized_df.mul(weights.values.reshape(-1)) return weighted_normalized_df def determine_ideal_solutions(weighted_normalized_df, impacts): """确定正理想解和负理想解""" positive_ideal_solution = weighted_normalized_df.max().where( impacts == '+', weighted_normalized_df.min()) negative_ideal_solution = weighted_normalized_df.min().where( impacts == '+', weighted_normalized_df.max()) pis = positive_ideal_solution.fillna(positive_ideal_solution.mean()) nis = negative_ideal_solution.fillna(negative_ideal_solution.mean()) return pis, nis def compute_separations(weighted_normalized_df, pis, nis): """计算分离度""" s_pis = ((weighted_normalized_df - pis) ** 2).sum(axis=1) ** 0.5 s_nis = ((weighted_normalized_df - nis) ** 2).sum(axis=1) ** 0.5 return s_pis, s_nis def calculate_closeness_coefficients(s_pis, s_nis): """计算相对接近度系数""" cc = s_nis / (s_pis + s_nis) return cc def topsis_method(df, weights, impacts): """ 使用Topsis方法评估给定的数据框df， 权重weights表示各个指标的重要性程度, 影响impacts表示每个标准是收益型('+')还是成本型('-') """ # 数据预处理 df_copy = df.copy() normalized_df = normalize_data(df_copy) # 计算加权规范化决策矩阵 weighted_normalized_df = calculate_weighted_normalized_matrix(normalized_df, weights) # 确定理想解与反理想解 pis, nis = determine_ideal_solutions(weighted_normalized_df, impacts) # 计算分离度 s_pis, s_nis = compute_separations(weighted_normalized_df, pis, nis) # 计算相对贴近度 cc = calculate_closeness_coefficients(s_pis, s_nis) result = pd.DataFrame({ 'Separation from Positive Ideal': s_pis, 'Separation from Negative Ideal': s_nis, 'Closeness Coefficient': cc}) ranked_result = result.sort_values(by='Closeness Coefficient', ascending=False) return ranked_result if __name__ == "__main__": # 示例输入 criteria_weights = np.array([0.25, 0.25, 0.25, 0.25]) criterion_impact = ['+', '-', '+', '-'] decision_matrix = [[7, 8, 9, 6], [4, 3, 2, 5], [8, 7, 6, 9]] df_input = pd.DataFrame(decision_matrix, columns=['A', 'B', 'C', 'D']) results = topsis_method(df_input, criteria_weights, criterion_impact) print(results) ``` 此段代码实现了完整的Topsis流程，包括数据标准化、构建加权规范化决策矩阵、确定理想解和非理想解、计算距离以及最终得出相对贴近度并排序[^1]。