Analytic Hierarchy Process Model (AHP)

The following is my game content of the paper:

1.1 Data Selector

        First, find out the various provinces in the national economy Statistical Yearbook economic and environmental indicators, the two can interact with tertiary index hierarchy analysis and evaluation models form the economic and environmental aspects of the chosen model of economic indicators for local Finance travel tax (million), special local fiscal revenue (million), state-owned local financial resources (assets) paid use revenue (million), local finance other non-tax revenue (million), per capita disposable income (yuan ), per capita disposable income (yuan), selected environmental indicators for the sulfur dioxide emissions (tons), nitrogen oxide emissions (tons), lead emissions (kg), mercury emissions (kg).

1.2 Analysis Hierarchy Process model building step

1.2.1 delivery times established class structure

        The factors involved in the problem of structured, hierarchical, construct a hierarchical structure model, the model in this complex problem is decomposed into several elements, have a certain relationship between the various levels, on an element level there are a dominant element to the next level, the level can be divided into the following three categories: the top, middle layer, the lowest layer. The hierarchical structure of the establishment has the following features:

1. Throughout the structure, the number of levels is not limited;
2. The highest level is only one element, each element of the dominant element is generally not more than 9;
3. Domination relationship exists from top to bottom order, and is represented by straight line segments;
4. Having a hierarchical structure can be introduced into the dummy sub-elements;

1.2.2 parity judgment matrix configuration twenty-two

        We depending on the circumstances, given dominant factor which is more important, given the judgment matrix. Judgment matrix has

Matrix having such properties is referred to as positive reciprocal matrix, the weight table is given below:

1.2.3 single element relative weight criterion recalculation

(1) the sum method

         N matrices is determined to take the normalized column vectors of the arithmetic operation after a weight vector as an approximate mean value of both:

(2) Genfa

        The respective vector matrix is ​​determined using the geometric mean of the normalized column vectors obtained approximated as a weight vector.

 

(3) Method Eigenvalue

        Eigenvector matrix determined after the first largest eigenvalue and right eigenvectors, and then sort the normalized weight vector.

1.2.4 Consistency Check

        1. Calculate the consistency index

        2. Find the corresponding average random consistency index RI

 

1.3 Environmental and Economic analytic hierarchy model

1.3.1 to determine the evaluation index

       国内对于个体评估研究还没有统一的指标体系，一般是按照作者主观选取有一定的关系，本文选取的评价指标见下表：

 1.3.2指标权重体系的构建

        采用层次分析法将各省层次评估模型评价体系中一级系统、二级、三级子系统指标因子的重要性进行两两比较，构造判别矩阵，得出如下指标权重表所示。

1.3.3消除量纲的影响 

        由于原始数据量纲各不相同，不能直接数学模型计算，为方便我们采用最大值法进行评价，具有正相关的指标标准化计算公式为：

对于具有相反相关性的指标进行逆处理，公式为：

1.3.4计算各层元素对目标层的合成权重

        将各指标的权重、指标原始数据无量纲化化之后，通过计算综合值，得出综合评价。

        采用线性加权求和计算模型进行计算：

这样从第三级指标开始，计算上一层的指标，再有上一层的权重乘以评价值，通过线性加权求和，算出最顶层指标值，即为个体评估得分。

1.4模型的结果

        根据以上步骤可以得出如下各省份经济和环境的综合指标排序情况，以经济和环境的权重系数都为0.5，根据以上得出排序指标如下：

        从以上分析知，模型综合了经济指标和环境指标两方面算出综合评价值，从表17中可以看出上海市综合指标值为0.769，综合排序为第一，首先对于上海是沿海城市，海陆交通便利，上海也邻近沪宁杭工业基地，工业基础好，上海经济发达，科研基地多，有良好的科技基础、上海市吸引力强，有大批人才，有利于发展。从这几方面可以看出上海经济方面是非常强的，上海市政府对于环境的治理也实施者重大措施，故才使上海在环境和经济方面综合排序值为第一位。北京、浙江、天津依次排位第2、3、4。而排在最后的是贵州和云南，由于交通不便致使环境和经济的总排序比较落后，其综合排序值分别为0.368、0.361。

1.5 相关代码：

经济指标权重系数表：
clear
clc
a=[1,1,1,4,1,1/2;1,1,2,4,1,1/2;1,1/2,1,5,3,1/2;1/4,1/4,1/5,1,1/3,1/3;1,1,1/3,3,1,1;2,2,2,3,3,1];
[x,y]=eig(a);
eigenvalue=diag(y);
lamda=eigenvalue(1);     %矩阵a的最大特征值
ci1=(lamda-6)/5        %一致性指标CI
cr1=ci1/1.26            %一致性比率CR，如果小于0.1，则通过一致性检验。
w1=x(:,1)/sum(x(:,1))    %相应的特征向量W1

环境指标权重系数表：
clear
clc
a=[1 2 2 3;1/2 1 2 5;1/2 1/2 1 4;1/3 1/5 1/4 1];
[x,y]=eig(a);
eigenvalue=diag(y);
lamda=eigenvalue(1);     %矩阵a的最大特征值
ci1=(lamda-4)/3         %一致性指标CI
cr1=ci1/0.89             %一致性比率CR，如果小于0.1，则通过一致性检验。
w1=x(:,1)/sum(x(:,1))    %相应的特征向量W1

计算经济与环境综合评价指标值：
clear
clc
num=xlsread('问题三.xls');
m=max(num);
A1=[];
for i=1:6
  a=num(:,i)./m(i);
  A1=[A1,a];
end
B2=[];
for j=7:10
  b=num(:,j)./m(j);
  B2=[B2,b];
end
B1=1-B2;
F1=[];
for k=1:31  f=0.1507.*A1(k,1)+0.1792.*A1(k,2)+0.1886.*A1(k,3)+0.0472.*A1(k,4)+0.1464.*A1(k,5)+0.2879.*A1(k,6);
  F1=[F1;f];%经济综合评价指标值
end
F2=[];
for k1=1:31
f1=0.3996.*B1(k1,1)+0.3142.*B1(k1,2)+0.2086.*B1(k1,3)+0.0776.*B1(k1,4);
F2=[F2;f1];%环境综合指标评价值
end
F=[];
f2=1/2.*(F1+F2);
F=[F;f2];%环境与经济综合评价指标值