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⛄ 内容介绍
目前的研究旨在提出一种新的方法，称为序列优先级方法（OPA）在多个属性决策（MADM）中。该方法可用于个人或组决策（GDM）。在GDM的情况下，通过这种方法，我们首先确定专家及其优先事项。专家的优先级可以根据他们的经验和/或知识确定。经过专家的优先级，每个专家优先考虑该属性。同时，每个专家都基于每个属性排名替代方案，如果有的话，子属性。最终，通过求解该方法的呈现的线性编程模型，将同时获得属性，替代品，专家和子属性的权重。所提出的方法的显着优点是它不利用成对比较矩阵，决策矩阵（无需数值输入），归一化方法，用于聚合专家意见（以GDM）和语言变量的平均方法。这种方法的另一个优点是专家只对他们有足够的知识和经验的属性和替代方案发表评论。使用几个组和个别实例评估了所提出的模型的有效性。最后，将所提出的方法与其他方法进行比较，例如AHP，BWM，Topsis，Vikor，Promethee和Perquiflex。基于使用Spearman和Pearson相关系数的重量和级别的比较，该方法与其他方法相比具有适用的性能。
⛄ 完整代码
close all
clear
clc
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Please study the user manual file before start working
%Contact with pmp.mahmoudi@gmail.com if you have problem to use this file
%Reference:
%Ataei, Y., Mahmoudi, A., Feylizadeh, M. R., & Li, D. F. (2020). Ordinal Priority Approach (OPA) in Multiple Attribute Decision-Making. Applied Soft Computing, 86, 105893.
%website: www.ordinalpriorityapproach.com
ee= input('Enter the preference matrix of experts: ');
ii= input('Enter the preference matrix of criteria by experts: ');
criteria_alternate_mat = input('Enter the preference matrix of alternatives in all criteria by experts: ');
experts=size(ee,2);
criteria=size(ii,2);
alternatives=size(criteria_alternate_mat,1)/experts;
%%
%construct matrix of Inequalities
C = {};
index_temp = 0;
for e = 1:experts
criteria_alternate_mat_temp = criteria_alternate_mat((e-1)*alternatives+1:e*alternatives,:);
for i = 1:criteria
index_temp = index_temp +1;
mini_A = zeros(alternatives,alternatives);
for j = 1: alternatives
if j == alternatives
index = find(criteria_alternate_mat_temp(:,i)==alternatives);
mini_A(j,index) = ee(e)*ii(e,i)*j;
break
end
for k = j:j+1
index = find(criteria_alternate_mat_temp(:,i)==k);
if k== j
mini_A(j,index) = ee(e)*ii(e,i)*j;
elseif k==j+1
mini_A(j,index) = -(ee(e)*ii(e,i)*j);
end
end
end
C{index_temp} = mini_A;
end
end
%%
A = blkdiag(C{:});
%% cost fucntion
f = -[1,zeros(1,experts*criteria*alternatives)]';
%%
A = [ones(experts*criteria*alternatives,1),-A];
b = zeros(1,experts*criteria*alternatives)';
%construct vector equal constrain
beq = 1;
Aeq = [0,ones(1,experts*criteria*alternatives)];
lb = [-Inf,zeros(1,experts*criteria*alternatives)];
%%
%solve the problem
x = linprog(f,A,b,Aeq,beq,lb);
%% compute weights
Z_optimal = x(1,1)
x_weight = x(2:experts*criteria*alternatives+1,1)
%compute w for experts
w_expetrs = mat2cell(x_weight,criteria*alternatives*ones(1,experts));
for i = 1:experts
disp(['Expert number ' ,num2str(i),' :'])
expert = sum(w_expetrs{i})
end
%compute w for criteria
w_criteria_mat= zeros(experts,criteria);
for i = 1:experts
w_criteria = mat2cell(w_expetrs{i},alternatives*ones(1,criteria));
for j=1:criteria
w_criteria_mat(i,j) = sum(w_criteria{j});
end
end
disp('vector of criteria is:')
w_criteria_final = sum(w_criteria_mat,1)
%%
%compute w for alternatives
for i = 1:alternatives
index = [i:alternatives:experts*criteria*alternatives];
disp(['Alternative number ' ,num2str(i),' :'])
alt_ans = sum(x_weight(index))
end
⛄ 参考文献
Ataei, Y., Mahmoudi, A., Feylizadeh, M. R., & Li, D. F. (2020). Ordinal Priority Approach (OPA) in Multiple Attribute Decision-Making. Applied Soft Computing, 86, 105893.
