用模糊控制boston housing数据集进行回归（Python语言来编写程序）

好的，我来回答您的问题。

首先，您需要安装模糊控制库 `scikit-fuzzy`，可以使用以下命令进行安装：

pip install -U scikit-fuzzy

接下来，您需要准备Boston Housing数据集。可以使用以下代码进行下载和加载：

from sklearn.datasets import load_boston

boston = load_boston()

X = boston.data
y = boston.target

接着，您需要对数据进行归一化处理，可以使用 `MinMaxScaler` 进行处理：

from sklearn.preprocessing import MinMaxScaler

scaler = MinMaxScaler()
X = scaler.fit_transform(X)

然后，您需要定义模糊控制系统的输入和输出变量。我们假设有三个输入变量：房间数、税收和犯罪率，一个输出变量：房价。可以使用以下代码进行定义：

import numpy as np
import skfuzzy as fuzz

# Define input variables
rooms = np.arange(1, 11, 1)
tax = np.arange(0, 1.1, 0.1)
crime = np.arange(0, 1.1, 0.1)

# Define output variable
price = np.arange(0, 51, 1)

接着，您需要定义每个变量的隶属度函数。可以使用以下代码进行定义：

# Define membership functions for each variable
rooms_low = fuzz.trimf(rooms, [1, 1, 5])
rooms_med = fuzz.trimf(rooms, [1, 5, 10])
rooms_high = fuzz.trimf(rooms, [5, 10, 10])

tax_low = fuzz.trimf(tax, [0, 0, 0.5])
tax_med = fuzz.trimf(tax, [0, 0.5, 1])
tax_high = fuzz.trimf(tax, [0.5, 1, 1])

crime_low = fuzz.trimf(crime, [0, 0, 0.5])
crime_med = fuzz.trimf(crime, [0, 0.5, 1])
crime_high = fuzz.trimf(crime, [0.5, 1, 1])

price_low = fuzz.trimf(price, [0, 0, 25])
price_med = fuzz.trimf(price, [0, 25, 50])
price_high = fuzz.trimf(price, [25, 50, 50])

然后，您需要定义规则库，将输入变量映射到输出变量。可以使用以下代码进行定义：

# Define rules
rule1 = np.fmax(rooms_low, np.fmax(tax_low, crime_low))
rule2 = np.fmax(rooms_med, np.fmax(tax_med, crime_med))
rule3 = np.fmax(rooms_high, np.fmax(tax_high, crime_high))

# Define output membership functions for each rule
out_low = np.fmin(rule1, price_low)
out_med = np.fmin(rule2, price_med)
out_high = np.fmin(rule3, price_high)

# Aggregate all output membership functions
aggregated = np.fmax(out_low, np.fmax(out_med, out_high))

# Calculate defuzzified output value
result = fuzz.defuzz(price, aggregated, 'centroid')

最后，您可以将以上代码整合为一个函数，并使用交叉验证等技术对模型进行评估。完整代码如下：

import numpy as np
import skfuzzy as fuzz
from sklearn.datasets import load_boston
from sklearn.preprocessing import MinMaxScaler
from sklearn.model_selection import cross_val_score

def fuzzy_regression(X, y):
    # Define input variables
    rooms = np.arange(1, 11, 1)
    tax = np.arange(0, 1.1, 0.1)
    crime = np.arange(0, 1.1, 0.1)

    # Define output variable
    price = np.arange(0, 51, 1)

    # Define membership functions for each variable
    rooms_low = fuzz.trimf(rooms, [1, 1, 5])
    rooms_med = fuzz.trimf(rooms, [1, 5, 10])
    rooms_high = fuzz.trimf(rooms, [5, 10, 10])

    tax_low = fuzz.trimf(tax, [0, 0, 0.5])
    tax_med = fuzz.trimf(tax, [0, 0.5, 1])
    tax_high = fuzz.trimf(tax, [0.5, 1, 1])

    crime_low = fuzz.trimf(crime, [0, 0, 0.5])
    crime_med = fuzz.trimf(crime, [0, 0.5, 1])
    crime_high = fuzz.trimf(crime, [0.5, 1, 1])

    price_low = fuzz.trimf(price, [0, 0, 25])
    price_med = fuzz.trimf(price, [0, 25, 50])
    price_high = fuzz.trimf(price, [25, 50, 50])

    # Define rules
    rule1 = np.fmax(rooms_low, np.fmax(tax_low, crime_low))
    rule2 = np.fmax(rooms_med, np.fmax(tax_med, crime_med))
    rule3 = np.fmax(rooms_high, np.fmax(tax_high, crime_high))

    # Define output membership functions for each rule
    out_low = np.fmin(rule1, price_low)
    out_med = np.fmin(rule2, price_med)
    out_high = np.fmin(rule3, price_high)

    # Aggregate all output membership functions
    aggregated = np.fmax(out_low, np.fmax(out_med, out_high))

    # Calculate defuzzified output value
    result = fuzz.defuzz(price, aggregated, 'centroid')

    return result

# Load Boston Housing dataset
boston = load_boston()
X = boston.data
y = boston.target

# Normalize input data
scaler = MinMaxScaler()
X = scaler.fit_transform(X)

# Evaluate model using cross-validation
scores = cross_val_score(fuzzy_regression, X, y, cv=10)
print("Accuracy: %0.2f (+/- %0.2f)" % (scores.mean(), scores.std() * 2))

希望这个回答对您有帮助！