层次分析法Python代码

层次分析法（Analytic Hierarchy Process，AHP）是一种用于多准则决策的方法，其目标是通过对准则的相对重要性进行定量评估，并对各个备选方案进行排序。下面是一个使用Python实现AHP的代码示例：

import numpy as np
from numpy import linalg

class AHP:
    def __init__(self, matrix):
        self.matrix = matrix

    def cal_weight_by_arithmetic_method(self):
        n = len(self.matrix)
        b = np.sum(self.matrix, axis=0)
        normal_a = self.matrix / b
        average_weight = np.mean(normal_a, axis=1)
        return average_weight

    def cal_weight_by_geometric_method(self):
        n = len(self.matrix)
        b = np.prod(self.matrix, axis=1)
        c = np.power(b, 1/n)
        average_weight = c / np.sum(c)
        return average_weight

    def cal_weight_by_eigenvalue_method(self):
        n = len(self.matrix)
        w, v = linalg.eig(self.matrix)
        eigenvalue = np.max(w)
        eigenvector = v[:, np.argmax(w)]
        average_weight = eigenvector / np.sum(eigenvector)
        return average_weight

# 示例用法
if __name__ == "__main__":
    b = np.array([[1, 1/3, 1/8], [3, 1, 1/3], [8, 3, 1]])
    ahp = AHP(b)
    weight1 = ahp.cal_weight_by_arithmetic_method()
    weight2 = ahp.cal_weight_by_geometric_method()
    weight3 = ahp.cal_weight_by_eigenvalue_method()

这段代码实现了AHP的算术平均法、几何平均法和特征值法，可以根据输入的判断矩阵计算出相应的权重。其中，`cal_weight_by_arithmetic_method()`函数实现了算术平均法，`cal_weight_by_geometric_method()`函数实现了几何平均法，`cal_weight_by_eigenvalue_method()`函数实现了特征值法。每个方法返回的是一个代表权重的一维数组。

请注意，代码中使用了NumPy库进行矩阵运算和线性代数计算。<span class="em">1</span><span class="em">2</span><span class="em">3</span>
#### 引用[.reference_title]
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