MCDM in the Selection of Doctor for an Illness: An Application of Electre

One of the sub-disciplines of operations research is Multiple-criteria decision-making (MCDM), which helps in making decisions about a problem in which there are multiple selection criterions. It is also known as Multiple-Criteria Decision Analysis (MCDA) as it helps to analyse a situation based on various parameters which are conflicting in nature and helps to decide which is better. Some of the popular MCDM methods include SAW [1, 2], TOPSIS [3], AHP [4], SMART [5], ELECTRE [6,7] etc. ELECTRE method is not just based on the cost function, but it compares each pair and finally presents the results. Decision-making problem provides various solutions which are called actions or alternatives. These actions, whether recorded comprehensively or not, must be formulated by the user. The outcomes of every one of them are assessed utilizing criteria. A criterion can be qualitative or quantitative and must be characterized by the user. When it is qualitative, the assessment of the actions on this criterion must be converted to a numerical scale. For example, let’s consider the criterion "Diagnosis Efficiency" for the selection of a doctor for a particular illness. Then this criterion should be first converted to numerical values scaling from 1 to 5. Also, weight is assigned to each criterion, which will increase based on its importance. For example, in selecting doctor diagnose efficiency of doctor is more important than experience so diagnose efficiency will be assigned more weight than experience. To use ELECTRE, we need the list of actions, the list of criteria, the evaluation of each action by criterion, and the weight of each criterion.

MCDM is not only helpful for industries or government, but it is also beneficial for taking daily life decisions. In this paper ELECTRE method has been used to select a doctor based on various criterions like Geographic location, Cost/Fees for the diagnosis, Consultation time given to the patient, Diagnosis efficiency of the doctor, Availability of the doctor and Doctor’s experience. Geographic location means the distance of patient to that doctor clinic or hospital, and it is a numerical criterion. Fees or cost includes prescriptions fees only, which is also a quantitative criterion. Consultation time means how much average time a doctor gives to his/her patient; this is also a quantitative criterion. Diagnosis efficiency means how much the prescribed medicines are useful, and this is a qualitative criterion, so it has been converted to a numerical value ranging from 1 to 5. Availability means how many days and every day how many hours the doctor is available. Whether the doctor provides emergency services or not. So this is a qualitative criterion and converted it to a numerical value ranging from 1 to 5. The last criterion is experience in years, and it is a quantitative value.

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Now out of these criterions most important one is Diagnosis efficiency, so it has been given 35% weight, next one is experience and availability, so 15% weightage given to each of them. Similarly,

Now the given details are to be converted to matrix form for different doctors. As shown below, columns represent criterion, i.e., Geographic Location, Cost, Consultation Time, Diagnosis Efficiency, Availability, and Experience, respectively. Similarly, rows represent different doctors. Here below is our decision matrix: And weights for each criterion are shown below:

function ELECTRE(X,W) Xval=length(X(:,1)); Y = zeros([Xval,length(W)]); for j=1:length(W) for i=1:Xval Y(i,j)=X(i,j)/sqrt(sum((X(:,j).^2))); end end Normalized_Matrix = num2str(Y); disp('Normalised Matrix :'); disp(Normalized_Matrix); for j=1:length(W) for i=1:Xval Yw(i,j)=Y(i,j).*W(j); end end Weighted_Normalized_Matrix = num2str([Yw]); fprintf('\nWeighted Normalised Matrix :\n'); disp(Weighted_Normalized_Matrix); %% CONCORDINATE SET CMat=zeros([Xval,Xval]); for i=1:Xval for j=1:Xval if i==j CMat(i,j) = 0; else sumOfWeights=0; for k=1:length(W) if Yw(i,k) >= Yw(j,k) sumOfWeights=sumOfWeights+W(k); end end CMat(i,j)=sumOfWeights; end end end fprintf('\nConcordance Matrix :\n') disp(CMat) sumOfColumn = sum(CMat); sumOfMatrix =sum(sumOfColumn); ratioOfConcordinateSet =sumOfMatrix/(Xval*2); CMatBinary=zeros([Xval,Xval]); for i=1:Xval for j=1:Xval if CMat(i,j)>=ratioOfConcordinateSet CMatBinary(i,j)=1; end end end disp('Concordance Matrix In Binary:') disp(CMatBinary) %% DISCORDANCE SET CMatDiff=zeros([Xval,Xval]); CMatTemp=zeros(1,length(W)); for i=1:Xval for j=1:Xval if i==j CMatDiff(i,j) = 0 ; else for k=1:length(W) CMatTemp(1,k) = Yw(i,k) - Yw(j,k);

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Here, finally a rank matrix is obtained. Rows and columns of this matrix represent doctors. Cells where value is 1 means that doctor at that row is preferable over the doctor represented by the column. In our case we are getting 1 in cells (2,1), (2,4), (3,1), (3,2), (3,4) and (4,1). This means that the doctor represented by row 2 has a higher preference than doctor 1. Similarly doctor 2 > doctor 4; doctor 3 > doctor 1; doctor 3 > doctor 2; doctor 3 > doctor 4; doctor 4 > doctor 1. So combining all these we get doctor 3 >doctor 2>doctor 4 >doctor 1.

In this paper an introduction of MCDM is given with special reference to a popular method, ELECTRE. A case study related to rank doctors to treat an illness based on certain criteria has been discussed. The same has been implemented using MATLAB and the experimental results have been discussed.

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Department of Computer Science, Aligarh Muslim University, Aligarh