Matlab tips (28) fuzzy comprehensive evaluation

Preface

MATLAB Learning about image processing is very friendly , You can start from scratch , There are many encapsulated functions that can be called directly for basic image processing , This series of articles is mainly to introduce some of you in MATLAB Some concept functions are commonly used in routine demonstration ！

Fuzzy comprehensive evaluation method is a comprehensive evaluation method based on Fuzzy Mathematics . The comprehensive evaluation method converts qualitative evaluation into quantitative evaluation according to the membership theory of Fuzzy Mathematics , That is to use fuzzy mathematics to make an overall evaluation of things or objects restricted by many factors . It has clear results , The characteristics of strong systematicness , It can better solve the fuzzy 、 Difficult to quantify , It is suitable for solving various uncertain problems .

The most remarkable feature of fuzzy comprehensive evaluation method is ：

1. Compare with each other
   Take the optimal evaluation factor value as the benchmark , Its evaluation value is 1; Other evaluation factors that are not optimal can get corresponding evaluation values according to the degree of suboptimal .

2. Function relation
   According to the characteristics of various evaluation factors , Determine the functional relationship between the evaluation value and the evaluation factor value （ namely ： Membership function ）. Determine this functional relationship （ Membership function ） There are many ways , for example ,F Statistical methods , All kinds of F Distribution, etc . Of course , Experienced bid evaluation experts can also be invited to evaluate , Directly give the evaluation value .

In the preparation of bidding documents , It should be based on the specific situation of the project , Select evaluation factors with emphasis , Scientifically determine the functional relationship between the evaluation value and the evaluation factor value, and reasonably determine the weight of the evaluation factor . General steps of fuzzy comprehensive evaluation ：

1. Construction of fuzzy comprehensive evaluation index
   Fuzzy comprehensive evaluation index system is the basis of comprehensive evaluation , Whether the selection of evaluation indicators is appropriate , It will directly affect the accuracy of the comprehensive evaluation . The construction of the evaluation index should widely involve the industry data of the evaluation index system or relevant laws and regulations .

2. Use to build a good weight vector
   Through expert experience or AHP The analytic hierarchy process constructs the weight vector .

3. Construct membership matrix
   Establish a suitable membership function to construct a membership matrix .

4. Synthesis of membership matrix and weight
   It is synthesized with suitable synthesis factors , And explain the result vector .

Simulation example MATLAB Version is MATLAB2015b.

One . MATLAB Simulation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： This procedure is a fuzzy comprehensive evaluation procedure , Artificial weight 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-27
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% I.  Clear environment variables 
clear all
clc

tic
%--------------------------------------------------------------------------
% The program runs , Enter the command directly mohu that will do 
% This program can be extended 
% For the two-level fuzzy comprehensive evaluation , Can be compiled mohufun.m Function to implement 
% Such as [yy1,qdh,qdh1]=mohufun(R,L,M,w,XX,yy] To run this function twice , And prepare corresponding m file , Two of these functions can be implemented 
% The result of fuzzy evaluation shows ：
%1: The sum of membership degrees for all levels is 1.
%2： The output results increase with the increase of a variable qdh1 The result shows monotonic increasing or decreasing 
%3: The final grade is [0.2 0 0 0.8] This is normal , It is different from the concept of hierarchical distance in extension evaluation .
% Only variables belong to 0.2 At this level .
%--------------------------------------------------------------------------

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This part is calculated by , Artificially given part , That is, the relevant solution conditions 
% It is required to input part before calculation 
R=4;  % Number of influencing factors 
L=4;  % The number of grades of judgment 
M=29; % Number of tunnel sections to be evaluated 
w=[0.1 0.7 0.1 0.1];% Weight of each indicator 
% Classical domain of extension evaluation , Form a group every day , share L Group , From left to right, it is 1,2,3,4
% The judgment result is 1, Means it belongs to the leftmost classical field , by 4 Belongs to the rightmost classical field 
%XX Is the range of membership function , For details, please refer to fuzzy comprehensive evaluation based on rough set , One has four membership functions 
% The first two numbers , Determine the membership function of a descending segment , It's divided into three parts 
% In the future 4 The upper number is a group , Determine a trapezoidal membership function , Divided into five sections 
% The last two are a separate group , The membership function of a rising segment is divided into three segments 
% Each line below has 12 Number , Its share 4 Level , Count the number of points in the division 2 4 4 2  The sum is 12
% That is to say, it forms four levels 
%XX It is also the core data of calculation 
xx=[70	90	70	90	110	130	110	130	170	190	170	190
   45	35	45	35	30	20	30	20	17	10	17	10
  1.5	2.5	1.5	2.5	3	4	3	4	4.5	5.5	4.5	5.5
0.25	0.35	0.25	0.35	0.45	0.55	0.45	0.55	0.65	0.75	0.65	0.75];

%pp1 The bigger the index is , The higher the rank , Or the bigger , The smaller the grade is 
%0 The larger the index value , The higher the level 
%1 The larger the index value , The lower the grade 
% This point should be strictly implemented ,XX（i,:), From small to large 0,XX（i,:) From big to small 1,
% If the above XX The order of line is reversed , Then for pp1=[1 0 1 1 ]
pp1=[0 1 0 0];
% Parameters of each tunnel section to be evaluated 
yy=[200	8	6	0.8
200	9.5	6	0.8
200	11	6	0.8
200	12.5	6	0.8
200	14	6	0.8
200	15.5	6	0.8
200	17	6	0.8
200	18.5	6	0.8
200	20	6	0.8
200	21.5	6	0.8
200	23	6	0.8
200	24.5	6	0.8
200	26	6	0.8
200	27.5	6	0.8
200	29	6	0.8
200	30.5	6	0.8
200	32	6	0.8
200	33.5	6	0.8
200	35	6	0.8
200	36.5	6	0.8
200	38	6	0.8
200	39.5	6	0.8
200	41	6	0.8
200	42.5	6	0.8
200	44	6	0.8
200	45.5	6	0.8
200	47	6	0.8
200	48.5	6	0.8
200	50	6	0.8
];
% The membership function form of the ascending and descending segments 
% Note that the form of membership function is the same as that in the paper , Otherwise, change the basic parts of the program 
% there a It refers to the middle point of the interval ,b Refers to the width of the interval 
f1=inline('0.5-0.5*sin((x-a)*pi/b)','a','b','x');
f2=inline('0.5+0.5*sin((x-a)*pi/b)','a','b','x');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Find the membership degree of each index for the first grade 
for i=1:M,
    for k=1:R,
        j=1;
        if pp1(k)==0     % First, the bigger , The higher the level is     
          if yy(i,k)<xx(k,j)
              yy1(i,k,j)=1;
          elseif yy(i,k)<=xx(k,j+1)
              yy1(i,k,j)=f1(0.5*(xx(k,j)+xx(k,j+1)),abs(xx(k,j)-xx(k,j+1)),yy(i,k)) ;
          else yy1(i,k,j)=0;
          end
% The smaller the evaluation , The higher the level is 
% Compared with one, greater than and less than are interchangeable , function f1 and f2 Also exchange 
        elseif yy(i,k)>xx(k,j)
              yy1(i,k,j)=1;
        elseif yy(i,k)>=xx(k,j+1)
             yy1(i,k,j)=f2(0.5*(xx(k,j)+xx(k,j+1)),abs(xx(k,j)-xx(k,j+1)),yy(i,k));  
        else yy1(i,k,j)=0;
        end
     end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate the membership degree of each index for the last grade 
 for i=1:M,
    for k=1:R,
        j=L;
        if pp1(k)==0       % First, the bigger , The higher the level is  
          if yy(i,k)<xx(k,j*4-5)
             yy1(i,k,j)=0;
          elseif yy(i,k)<=xx(k,j*4-4)
             yy1(i,k,j)=f2(0.5*(xx(k,j*4-5)+xx(k,j*4-4)),abs(xx(k,j*4-5)-xx(k,j*4-4)),yy(i,k));  
          else yy1(i,k,j)=1;
          end

% The smaller the evaluation , The higher the level is 
% Compared with one, greater than and less than are interchangeable , function f1 and f2 Also exchange 
        elseif yy(i,k)>xx(k,j*4-5)
               yy1(i,k,j)=0;
        elseif yy(i,k)>=xx(k,j*4-4)
               yy1(i,k,j)=f1(0.5*(xx(k,j*4-5)+xx(k,j*4-4)),abs(xx(k,j*4-5)-xx(k,j*4-4)),yy(i,k)) ; 
        else yy1(i,k,j)=1;
        end
     end
 end   
    
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Find the membership degree of each index for the middle levels 
 for i=1:M,
    for k=1:R,
        for j=2:L-1;     
           if pp1(k)==0     % First, the bigger , The higher the level is  
             if yy(i,k)<xx(k,j*4-5)
                yy1(i,k,j)=0;
             elseif yy(i,k)<=xx(k,j*4-4)
                    yy1(i,k,j)=f2(0.5*(xx(k,j*4-5)+xx(k,j*4-4)),abs(xx(k,j*4-5)-xx(k,j*4-4)),yy(i,k));  
             elseif yy(i,k)<=xx(k,j*4-3)
                    yy1(i,k,j)=1;
             elseif yy(i,k)<=xx(k,j*4-2)
                    yy1(i,k,j)=f1(0.5*(xx(k,j*4-3)+xx(k,j*4-2)),abs(xx(k,j*4-3)-xx(k,j*4-2)),yy(i,k)) ;    
             else yy1(i,k,j)=0;
             end
% The smaller the evaluation , The higher the level is 
% Compared with one, greater than and less than are interchangeable , function f1 and f2 Also exchange 
           elseif yy(i,k)>xx(k,j*4-5)
                  yy1(i,k,j)=0;
           elseif yy(i,k)>=xx(k,j*4-4)
                  yy1(i,k,j)=f1(0.5*(xx(k,j*4-5)+xx(k,j*4-4)),abs(xx(k,j*4-5)-xx(k,j*4-4)),yy(i,k));
           elseif yy(i,k)>=xx(k,j*4-3)
                  yy1(i,k,j)=1;
           elseif yy(i,k)>=xx(k,j*4-2)
                  yy1(i,k,j)=f2(0.5*(xx(k,j*4-3)+xx(k,j*4-2)),abs(xx(k,j*4-3)-xx(k,j*4-2)),yy(i,k)) ;   
           else yy1(i,k,j)=0;
           end              
        end 
    end
end
 
 % % Multiply by , The membership degree multiplies the weight, and the membership degree of each hole section to each grade , Taking the maximum 
 %dot Function is inner product function , Sum the two vectors after their corresponding components are equal 
for i=1:M,
   for j=1:L,    
        qdh(i,j)=dot(yy1(i,:,j),w);           
   end
end
% Multiply the membership by the grade value , Determine level 
% %qdh For the evaluation results , Take one of the biggest , Which level does it belong to 
% qdh1, Rank value 

 for i=1:M,
   for j=1:L,       
         [maxlevel(i),qdh1(i)]=max(qdh(i,:));  
   end
    disp([' sample ',num2str(i),' The corresponding classification is ：',num2str(qdh1(i))]); 
 end

figure(1)
plot(qdh1(1:29),'-*');
title(' Fuzzy comprehensive evaluation prediction ','fontsize',12)
xlabel(' sample ','fontsize',12)
ylabel(' Category ','fontsize',12)
 
toc

Two . Simulation results

 sample 1 The corresponding classification is ：4
 sample 2 The corresponding classification is ：4
 sample 3 The corresponding classification is ：4
 sample 4 The corresponding classification is ：4
 sample 5 The corresponding classification is ：4
 sample 6 The corresponding classification is ：3
 sample 7 The corresponding classification is ：3
 sample 8 The corresponding classification is ：3
 sample 9 The corresponding classification is ：3
 sample 10 The corresponding classification is ：3
 sample 11 The corresponding classification is ：3
 sample 12 The corresponding classification is ：3
 sample 13 The corresponding classification is ：2
 sample 14 The corresponding classification is ：2
 sample 15 The corresponding classification is ：2
 sample 16 The corresponding classification is ：2
 sample 17 The corresponding classification is ：2
 sample 18 The corresponding classification is ：2
 sample 19 The corresponding classification is ：2
 sample 20 The corresponding classification is ：2
 sample 21 The corresponding classification is ：2
 sample 22 The corresponding classification is ：2
 sample 23 The corresponding classification is ：1
 sample 24 The corresponding classification is ：1
 sample 25 The corresponding classification is ：1
 sample 26 The corresponding classification is ：1
 sample 27 The corresponding classification is ：1
 sample 28 The corresponding classification is ：1
 sample 29 The corresponding classification is ：1
 Time has passed  0.075994  second .

3、 ... and . Summary

Fuzzy comprehensive evaluation method （fuzzy comprehensive evaluation method） It is one of the most basic mathematical methods in Fuzzy Mathematics , This method uses membership degree to describe fuzzy bounds . Due to the complexity of evaluation factors 、 The hierarchy of the evaluation object 、 The fuzziness in the evaluation criteria and the fuzziness or uncertainty of the evaluation influencing factors 、 A series of problems such as difficulty in quantifying qualitative indicators , It makes it difficult for people to use absolute “ either this or that ” To accurately describe the objective reality , There are often “ This is the same as that ” Fuzzy phenomenon of , Its description is often expressed in natural language , The biggest feature of natural language is its fuzziness , And this kind of fuzziness is difficult to be measured uniformly by classical mathematical models . therefore , Fuzzy comprehensive evaluation method based on fuzzy set , Comprehensively evaluate the subordinate level of the evaluated things from multiple indicators , It divides the change range of the judged things , On the one hand, we can take into account the hierarchy of objects , Make the evaluation criteria 、 The fuzziness of influencing factors is reflected ; On the other hand, we can give full play to people's experience in evaluation , Make the evaluation results more objective , In line with the actual situation . Fuzzy comprehensive evaluation can combine qualitative and quantitative factors , Expand the amount of information , So that the number of evaluations can be improved , The evaluation conclusion is credible .

There are many traditional comprehensive evaluation methods , It is also widely used , But there is no way to suit all kinds of places , Solve all the problems , Each method has its focus and main application fields . If we want to solve new problems in new fields , Fuzzy synthesis method is obviously more suitable . Fuzzy evaluation method is based on Fuzzy Mathematics . Fuzzy mathematics was born in 1965 year , His founder, American automatic control expert L.A.Zadeh.20 century 80 Late S , Japan applies fuzzy technology to robots 、 process control 、 Subway locomotive 、 traffic control 、 Troubleshooting 、 Medical diagnosis 、 Voice recognition 、 The image processing 、 Market prediction and many other fields . The application of fuzzy theory and fuzzy method in Japan and its huge market prospect , It has shocked the Western business community , It has also been widely recognized in academia . Domestic research on fuzzy mathematics and fuzzy comprehensive evaluation method started relatively late , But in recent years, in various fields （ Such as medicine 、 The construction industry 、 Environmental quality supervision 、 Water conservancy, etc ） The application of has also shown initial results . Learn one every day MATLAB Little knowledge , Let's learn and make progress together ！