1. 前言

最近小白在跟进一个项目，其中运用到了灰色关联分析法用来分析样本数据。同时在阅读了一些原理资料后，设计了一个模块化的C++程序(其实也不算模块化啦)，关于原理方面，我在这里就不过多的赘述了，想要了解原理的同学，可以移步到下面的链接去了解。接下来我就把我编写的算法程序分享给大家。

2. 理论基础

链接：原理链接1、原理链接2

3. 代码

（1）.h文件：

#pragma once
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>using namespace std;class GRA
{
public:GRA();void SetTargetSequence(vector<double> target_);//设置目标序列void SetIndexSequence(vector<vector<double>> index_);//设置样本序列void SetWeight(vector<double> w);//设置权重double PolarityMin(vector<double> targetIndex_);//数据标准化double PolarityMax(vector<double> targetIndex_);//数据标准化double IndexMax(vector<double> targetIndex_);//数据标准化double IndexMin(vector<double> targetIndex_);//数据标准化void ForwardProcessing(vector<double> &index_, int num);//数据正向化void MaximumDimensionless(vector<double> &index_);//数据标准化void MinimumDimensionless(vector<double>& index_);//数据标准化void PushIndex(vector<double> index_);vector<vector<double>> TransPose(vector<vector<double>> index_);//转置void GreyRelationCompute();//灰色关联度计算vector<double> GetGreyRelation();//输出关联度向量vector<vector<double>> GetRelationMatrix();//输出关联度矩阵(用于检测数据计算准确性)private:vector<double> weight;//权重double row;vector<double> targetSequence;//目标序列vector<vector<double>> indexSequence;//样本序列vector<vector<double>> relationMatrix;//关联度矩阵vector<double> relation;//关联度向量};

（2）.cpp文件：

#include <iostream>
#include <vector>
#include "GRA.h"using namespace std;GRA::GRA()
{row = 0.5;}void GRA::SetTargetSequence(vector<double> target_)
{targetSequence = target_;
}void GRA::SetIndexSequence(vector<vector<double>> index_)
{indexSequence = index_;
}void GRA::SetWeight(vector<double> w)
{weight = w;
}double GRA::PolarityMax(vector<double> targetIndex_)
{double tmp = fabs(targetSequence[0] - targetIndex_[0]);for (int i = 0; i < targetIndex_.size(); i++){if (tmp < (fabs(targetSequence[i] - targetIndex_[i]))){tmp = fabs(targetSequence[i] - targetIndex_[i]);}}return tmp;}double GRA::PolarityMin(vector<double> targetIndex_)
{double tmp = fabs(targetSequence[0] - targetIndex_[0]);for (int i = 0; i < targetIndex_.size(); i++){if (tmp > (fabs(targetSequence[i] - targetIndex_[i]))){tmp = fabs(targetSequence[i] - targetIndex_[i]);}}return tmp;}double GRA::IndexMax(vector<double> targetIndex_)
{double tmp = targetIndex_[0];for (int i = 0; i < targetIndex_.size(); i++){if (tmp < targetIndex_[i]){tmp = targetIndex_[i];}else{continue;}}return tmp;
}double GRA::IndexMin(vector<double> targetIndex_)
{double tmp = targetIndex_[0];for (int i = 0; i < targetIndex_.size(); i++){if (tmp > targetIndex_[i]){tmp = targetIndex_[i];}else{continue;}}return tmp;
}void GRA::ForwardProcessing(vector<double> &index_,int num)
{double Max = IndexMax(index_);for (int i = 0; i < index_.size(); i++){index_[i] = fabs(targetSequence[num] - index_[i]);}return;
}void GRA::MaximumDimensionless(vector<double>& index_)
{double MAX = IndexMax(index_);double MIN = IndexMin(index_);for (int i = 0; i < index_.size(); i++){index_[i] = (index_[i] - MIN) / (MAX - MIN);}return;
}void GRA::MinimumDimensionless(vector<double>& index_)
{double MAX = IndexMax(index_);double MIN = IndexMin(index_);for (int i = 0; i < index_.size(); i++){index_[i] = (MAX - index_[i]) / (MAX - MIN);}return;
}void GRA::PushIndex(vector<double> index_)
{indexSequence.push_back(index_);
}vector<vector<double>> GRA::TransPose(vector<vector<double>> index_)
{vector<vector<double>> result;for (int j = 0; j < index_[0].size(); j++){vector<double> tmp;for (int i = 0; i < index_.size(); i++){tmp.push_back(index_[i][j]);}result.push_back(tmp);}return result;
}void GRA::GreyRelationCompute()
{vector<vector<double>> Index = TransPose(indexSequence);//indexSequence 4x7，index 7x4vector<double> tmp_1, tmp_2;double memberReslution_1, memberReslution_2;for (int i = 0; i < Index.size(); i++){double member_1 = PolarityMin(Index[i]);double member_2 = PolarityMax(Index[i]);tmp_1.push_back(member_1);tmp_2.push_back(member_2);}memberReslution_1 = IndexMin(tmp_1);memberReslution_2 = IndexMax(tmp_2);for (int i = 0; i < Index.size(); i++){vector<double> re;/*re.push_back(i);*/for (int j = 0; j < Index[i].size(); j++){re.push_back((memberReslution_1 + row * memberReslution_2) / (fabs(targetSequence[j] - Index[i][j]) + (row * memberReslution_2)));}relationMatrix.push_back(re);}double tmp = 0;for (int i = 0; i < relationMatrix.size(); i++){for (int j = 0; j < relationMatrix[i].size(); j++){tmp += weight[j] * relationMatrix[i][j];}tmp = tmp / weight.size();relation.push_back(tmp);tmp = 0;}
}vector<double> GRA::GetGreyRelation()
{return relation;
}
vector<vector<double>> GRA::GetRelationMatrix()
{return relationMatrix;
}

（3）测试文件：

#include <iostream>
#include <vector>
#include "GRA.h"
#include <map>using namespace std;void main()
{vector<double> index_1, index_2, index_3, index_4, index_5, index_6, index_7;//样本数index_1.push_back(0);index_1.push_back(1);index_1.push_back(0.173);index_1.push_back(0.168);index_2.push_back(0);index_2.push_back(1);index_2.push_back(0.212);index_2.push_back(0.022);index_3.push_back(0);index_3.push_back(1);index_3.push_back(0.248);index_3.push_back(0.083);index_4.push_back(0);index_4.push_back(1);index_4.push_back(0.222);index_4.push_back(0.118);index_5.push_back(0);index_5.push_back(1);index_5.push_back(0.199);index_5.push_back(0.051);index_6.push_back(0);index_6.push_back(1);index_6.push_back(0.188);index_6.push_back(0.06);index_7.push_back(0);index_7.push_back(1);index_7.push_back(0.204);index_7.push_back(0.035);vector<vector<double>> index;for (int i = 0; i < index_1.size(); i++){vector<double> tmp;tmp.push_back(index_1[i]);tmp.push_back(index_2[i]);tmp.push_back(index_3[i]);tmp.push_back(index_4[i]);tmp.push_back(index_5[i]);tmp.push_back(index_6[i]);tmp.push_back(index_7[i]);index.push_back(tmp);}cout << index.size() << ", " << index[0].size() << endl;GRA A;vector<double> target;target.push_back(1);target.push_back(1);target.push_back(1);target.push_back(1);A.SetTargetSequence(target);A.ForwardProcessing(index[0], 0);A.MinimumDimensionless(index[2]);A.MinimumDimensionless(index[3]);vector<double> weight(4, 1);A.SetWeight(weight);A.SetIndexSequence(index);A.GreyRelationCompute();vector<vector<double>> relation = A.GetRelationMatrix();for (int i = 0; i < relation.size(); i++){for (int j = 0; j < relation[i].size(); j++){cout << relation[i][j] << ",\t";}cout << endl;}vector<double> path = A.GetGreyRelation();for (int i = 0; i < path.size(); i++){cout << path[i] << ",\t";}cout << endl;system("pause");return;
}

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灰色关联分析法(GRA)-C++实现

1. 前言

2. 理论基础

3. 代码

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