粗糙集属性约简

本实验同时采用区别矩阵和依赖度约简。
在依赖度约简中，设置依赖度计算函数和相对约简函数，对读取的数据进行处理，最后根据依赖度约简。
在读取数据后判断有无矛盾，若有则进行决策表分解，然后进行区别矩阵约简得到约简后的条件属性。

区分矩阵代码如下：

import xlrd #读取Excel的扩展工具
from copy import deepcopy
import numpy as np#numerical python
from pprint import pprint
import itertools

def read_excel(path):
    #打开excel
    x_matrix = []
    workbook = xlrd.open_workbook(path,'r') 
    table = workbook.sheets()[0] 
    for rown in range(1,table.nrows):
        x_matrix.append(table.row_values(rown))
    x_matrix = np.array(x_matrix)
    #print(x_matrix)
    return x_matrix

#决策表分解
def divide(matrix):
    len_attribute = len(matrix[0])-1
    matrix_delete = []
    #print(len(matrix))
    #决策表分解
    for j in range(len(matrix)):
        for k in range(j,len(matrix)):
            if ((matrix[j][0:len_attribute] == matrix[k][0:len_attribute]).all() and matrix[j][len_attribute] != matrix[k][len_attribute]):
                matrix_delete.append(list(matrix[j]))
                matrix_delete.append(list(matrix[k]))
                matrix = np.delete(matrix,k,axis=0)
                matrix = np.delete(matrix,j,axis=0)
    if(len(matrix_delete)):
        print('矛盾:',matrix_delete)
    else:
        print('不存在矛盾数据！')
        print('-------------------------------------------')
    
    if(len(matrix)):
        print('完全一致表:')
        pprint(matrix)
        deal(matrix)
    else:
        print('不存在完全一致表:')

    if(len(matrix_delete)):
        print('完全不一致表:')
        print(matrix_delete)

#约简
def deal(matrix):
    matrix_T = matrix.T
    number_sample = len(matrix)#样本数量
    number_attribute = len(matrix_T)-1#属性数量
    attribute = ['年龄','收入','学生','信誉']
    # 二维列表的创建：
    excel = [[ [] for col in range(number_sample)] for row in range(number_sample)] 
    pprint(matrix)
    #比较各样本哪些属性的值不同（只对决策属性不同的个体进行比较）
    for k in range(len(attribute)):#属性
        for i in range(number_sample):#第几个样本
            for j in range(i,number_sample):
                if(matrix[i][k] != matrix[j][k] and matrix[i][number_attribute] != matrix[j][number_attribute]):
                    excel[i][j].append(attribute[k])
    for i in range(number_sample):
        for j in range(i,number_sample):
            excel[j][i] = set(excel[i][j])
            excel[i][j] = {}
    #pprint(excel)#excel
    yuejian = []
    for i in range(number_sample):
        for j in range(number_sample):
            if(excel[i][j] and excel[i][j] not in yuejian):
                yuejian.append(excel[i][j])
    print(yuejian)
    #约简
    i=0
    j=0
    k=len(yuejian)#k=6
    for i in range(k):
        for j in range(k):
            if(yuejian[i] > yuejian[j]):#i更大，应该删除i
                yuejian[i] = yuejian[j]
            if(yuejian[i] & yuejian[j]):
                yuejian[i] = yuejian[i] & yuejian[j]
                yuejian[j] = yuejian[i] & yuejian[j]
    '''
    #print(yuejian)
    #去重
    yuejian_new = []
    for id in yuejian:
        if id not in yuejian_new:
            yuejian_new.append(id)
    yuejian = yuejian_new
    '''
    #print('约简为:',yuejian)
    #print('yuejian:',yuejian)
    #类似于笛卡儿积
    flag = 0
    result =[]
    for i in yuejian:
        if (len(i) > 1):
            flag = 1
    if(flag == 1):#将集合分解开，逐个取其与其他集合的并集
        simple = yuejian[0]
        nosimple = deepcopy(yuejian)
        i=0
        while (i < len(nosimple)):
            if(len(nosimple[i]) == 1):
                simple = simple | nosimple[i]
                nosimple.pop(i)
            else:
                i = i + 1
        for i in range(len(nosimple)):
            nosimple[i] = list(nosimple[i])
        simple = list(simple)
        
        for i in range(len(nosimple)):
            for j in range(len(nosimple[i])):
                simple_temp = deepcopy(simple)
                simple_temp.append(nosimple[i][j])
                result.append(simple_temp)
    else:
        simple = yuejian[0]
        for i in yuejian:
            simple = simple | i#如果只有单元素，则将取其与其他集合的并集
        result.append(list(simple))
    print(result)
    #约简矩阵的各属性的样本值
    matrix_new = []
    for i in range(len(result)):
        matrix_new.append([])
    for i in range(len(result)):
        for j in range(len(result[i])):
            for k in range(len(attribute)):
                if(result[i][j] == attribute[k]):
                    matrix_new[i].append(list(matrix_T[k]))
    #输出
    for i in range(len(matrix_new)):
        print('------------------------------------')
        print('序号 ',end='')
        for j in range(len(result[i])):
            print(result[i][j],'',end='')
        print(' 归类：买计算机?')
        for j in range(len(matrix_new[0][0])):
            print(j+1,end = '    ')
            for k in range(len(result[i])):
                print(matrix_new[i][k][j], end = '   ')
            print(' ',matrix[j][number_attribute])

if __name__ == '__main__':
    path = 'data.xlsx'
    # 读取数据
    matrix = read_excel(path)
    #deal(matrix)
    divide(matrix)    

依赖度约简代码如下：

from copy import deepcopy
import numpy as np
import pandas as pd
import xlrd
from pprint import pprint
from itertools import combinations, permutations
import random

#import 决策函数
def basic_set(df):
    basic = {}
    for i in df.drop_duplicates().values.tolist():
        basic[str(i)] = []
        for j, k in enumerate(df.values.tolist()):
            if k == i:
                basic[str(i)].append(j)
    return basic

def divide():
    path = 'data.xlsx'
    global matrix,mistake
    matrix = read_excel(path)
    len_attribute = len(matrix[0])-1
    matrix_delete = []
    #决策表分解
    mistake = []
    
    for j in range(len(matrix)):
        for k in range(j,len(matrix)):
            if ((matrix[j][0:len_attribute] == matrix[k][0:len_attribute]).all() and matrix[j][len_attribute] != matrix[k][len_attribute]):
                matrix_delete.append(list(matrix[j]))
                matrix_delete.append(list(matrix[k]))
                matrix = np.delete(matrix,k,axis=0)
                matrix = np.delete(matrix,j,axis=0)
                mistake.append(j)
                mistake.append(k)

    if(len(matrix_delete)):
        print('矛盾:',matrix_delete)
    else:
        print('不存在矛盾数据！')
        print('-------------------------------------------')
    if(len(matrix)):
        print('完全一致表:')
        pprint(matrix)
    else:
        print('不存在完全一致表:')

    if(len(matrix_delete)):
        print('完全不一致表:')
        print(matrix_delete)
    
def intersection_2(someone_excel):
    x_list = someone_excel[0]
    y_list = someone_excel[1]
    #print(x_list)
    #print(y_list)
    x_set = [[]]*len(x_list)
    for i in range(len(x_list)):
        x_set[i] = set(x_list[i])

    y_set = [[]]*len(y_list)
    for i in range(len(y_list)):
        y_set[i] = set(y_list[i])

    a = []
    for  i in range(len(x_list)):
        for  j in range(len(y_list)):
            if(x_set[i] & y_set[j]):
                a.append(x_set[i] & y_set[j])
    return a

def intersection(excel_temp):
    if (len(excel_temp)>1):
        a = intersection_2([excel_temp[0],excel_temp[1]])
        for k in range(2,len(excel_temp)):
            a = intersection([a,excel_temp[k]])
    else:
        a = excel_temp[0]
    return a

# 收集属性依赖性
def dependence_degree(x_list):
    count = 0 
    for i in x_list:
        for j in y_basic_list:
            if(set(i) <= set(j)):
                count = count + len(i)
    degree = round(count/len(x_data),4)
    return degree

def yilaidu_fun(k):
    excel_temp = list(combinations(excel,k))#排列组合数
    title_temp = list(combinations(title,k))
    for i in range(len(title_temp)):
        excel_temp[i] = list(excel_temp[i])
        title_temp[i] = list(title_temp[i])
    #print('title_temp:',title_temp)
    #print(excel_temp)
    a = []
    for i in range(len(excel_temp)):
        temp = intersection(excel_temp[i])
        #print(temp)
        print(title_temp[i],end=' ')
        print('依赖度:',dependence_degree(temp))
        if (dependence_degree(temp) == 1):
            a.append(set(title_temp[i]))
    #print(a)
    return a

def deal(data):
    data = data.dropna(axis=0, how='any')
    for i in sorted(mistake , reverse=True):
        data.drop(data.index[i], inplace=True)
    #使用pandas的loc来读取并把各属性值赋给变量（loc通过行标签索引数据）
    age_data = data.loc[:, 'C1']
    age_basic_list = sorted([v for k, v in basic_set(age_data).items() ])
    #print('age:',age_basic_list)

    income_data = data.loc[:, 'C2']
    income_basic_list = sorted([v for k, v in basic_set(income_data).items()])
    #print('income:',income_basic_list)

    student_data = data.loc[:, 'C3']
    student_basic_list = sorted([v for k, v in basic_set(student_data).items() ])
    #print('student_data',student_data)

    credit_data = data.loc[:, 'C4']
    credit_basic_list = sorted([v for k, v in basic_set(credit_data).items()])
    #print('student',credit_basic_list)
    
    global x_data,y_data,y_basic_list,excel
    x_data = data.drop(['judge'], axis=1)
    y_data = data.loc[:, 'judge']
    # 决策属性基本集
    y_basic_list = sorted([v for k, v in basic_set(y_data).items() ])
    #print(y_basic_list)

    excel = []
    excel.append(age_basic_list)
    excel.append(income_basic_list)
    excel.append(student_basic_list)
    excel.append(credit_basic_list)
    #print(excel)

    yilaidu = []
    for i in range(1,len(matrix)+1):
        yilaidu.extend(yilaidu_fun(i))
    print('依赖度为1的属性有:',yilaidu)
    #print(yilaidu)
    
    #约简
    i=0
    j=0
    k=len(yilaidu)#k=6
    for i in range(k):
        for j in range(k):
            if(yilaidu[i] > yilaidu[j]):#i更大，应该删除i
                yilaidu[i] = yilaidu[j]
    #去重
    yilaidu_new = []
    for i in yilaidu:
        if i not in yilaidu_new:
            yilaidu_new.append(i)
    for i in range(len(yilaidu_new)):
        yilaidu_new[i] = sorted(list(yilaidu_new[i]))
    result = yilaidu_new

    #各约简属性的属性值
    matrix_new = []
    for i in range(len(result)):
        matrix_new.append([])
    for i in range(len(result)):
        for j in range(len(result[i])):
            for k in range(len(title)):
                if(result[i][j] == title[k]):
                    matrix_new[i].append(list(matrix_T[k]))

    for i in range(len(matrix_new)):
        print('------------------------------------')
        print('序号 ',end='')
        for j in range(len(result[i])):
            print(result[i][j],'',end='')
        print('归类：买计算机?')
        for j in range(len(matrix_new[0][0])):
            print(j+1,end='    ')
            for k in range(len(result[i])):
                print(matrix_new[i][k][j], end = '  ')
            print(' ',matrix[j][len(matrix[0])-1])
    if(result == []):
        print('  年龄 收入 学生 信誉 归类：买计算机？')
        print(matrix)

def read_excel(path):
    #打开excel
    x_matrix = []
    workbook = xlrd.open_workbook(path,'r') 
    table = workbook.sheets()[0] 
    for rown in range(1,table.nrows):
        x_matrix.append(table.row_values(rown))
    x_matrix = np.array(x_matrix)
    #print(x_matrix)
    return x_matrix

def main():
    #读取文件数据
    data = pd.read_csv(filepath_or_buffer='data.CSV',encoding='unicode_escape')
    divide()
    global matrix_T 
    matrix_T = matrix.T
    len = data.iloc[:,0].size
    #数据集
    arr = data.iloc[0:len]
    global title 
    title= ['年龄','收入','学生','信誉']
    deal(arr)

if __name__ == '__main__':
    main()

测试表格如下：