grey and fuzzy TOPSIS

Hello ladies and gentlemen,

Please Kindly, can someone help me find a MATLAB code to solve the grey-TOPSIS method and the fuzzy-TOPSIS method?

Thank you so much

Answer 1

[Balavignesh]

Hi Ali,

The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a method used in multi-criteria decision making (MCDM). Grey-TOPSIS integrates the Grey System Theory with TOPSIS to deal with incomplete or uncertain information, where as Fuzzy-TOPSIS uses fuzzy numbers to represent decision matrix and weights, which allows to handle vagueness and subjectivity in the evaluation process.

Here is a rough implementation of the above mentioned concepts :

% Example Grey-TOPSIS Implementation in MATLAB
% This is a simplified example. Adapt it based on your specific criteria and alternatives.

% Define the decision matrix (alternatives x criteria)
% Assuming 3 alternatives and 4 criteria
D = [0.6 0.5 0.7 0.8; 0.9 0.7 0.6 0.5; 0.7 0.8 0.5 0.6];

% Define the weight for each criterion
W = [0.25 0.25 0.25 0.25]; % Equal weights for simplicity

% Normalize the decision matrix
row_sums = sqrt(sum(D.^2, 1));
N = D ./ row_sums;

% Calculate the weighted normalized decision matrix
V = N .* W;

% Determine the positive ideal (A+) and negative ideal (A-) solutions
A_plus = max(V, [], 1);
A_minus = min(V, [], 1);

% Calculate the distance to the positive ideal solution
D_plus = sqrt(sum((V - A_plus).^2, 2));

% Calculate the distance to the negative ideal solution
D_minus = sqrt(sum((V - A_minus).^2, 2));

% Calculate the similarity to the ideal solution
S = D_minus ./ (D_plus + D_minus);

% Rank the alternatives based on the similarity score
[~, rankIndex] = sort(S, 'descend');

% Display the ranking of alternatives
disp('Ranking of Alternatives:');

Ranking of Alternatives:

disp(rankIndex);

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% Example Fuzzy-TOPSIS Implementation in MATLAB
% This is a simplified example. You'll need to adapt it to your specific fuzzy numbers and context.

% Define the fuzzy decision matrix (alternatives x criteria)
% For simplicity, using direct numbers, but in practice, these should be fuzzy numbers
D = [0.6 0.5 0.7 0.8; 0.9 0.7 0.6 0.5; 0.7 0.8 0.5 0.6];

% Define the fuzzy weights for each criterion
W = [0.25 0.25 0.25 0.25]; % Equal weights for simplicity, should be fuzzy numbers

% Normalize the fuzzy decision matrix
% Note: The normalization process might be different based on the fuzzy number operations
row_sums = sqrt(sum(D.^2, 1));
N = D ./ row_sums;

% Calculate the fuzzy weighted normalized decision matrix
V = N .* W;

% Determine the fuzzy positive ideal (A+) and fuzzy negative ideal (A-) solutions
A_plus = max(V, [], 1);
A_minus = min(V, [], 1);

% Calculate the distance to the fuzzy positive ideal solution
D_plus = sqrt(sum((V - A_plus).^2, 2));

% Calculate the distance to the fuzzy negative ideal solution
D_minus = sqrt(sum((V - A_minus).^2, 2));

% Calculate the similarity to the ideal solution
S = D_minus ./ (D_plus + D_minus);

% Rank the alternatives based on the similarity score
[~, rankIndex] = sort(S, 'descend');

% Display the ranking of alternatives
disp('Ranking of Alternatives:');

Ranking of Alternatives:

disp(rankIndex);

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     3

Kindly note that these examples are simplified and intended to provide a basic structure. For both Grey-TOPSIS and Fuzzy-TOPSIS, the handling of grey numbers and fuzzy numbers, respectively, needs more detailed implementation based on your specific criteria, alternatives, and the nature of uncertainty or fuzziness in your decision-making context.

Kindly have a look at the following documentation links to have more information on:

• Fuzzy logic Toolbox: https://www.mathworks.com/products/fuzzy-logic.html
• Implementation of TOPSIS: https://www.youtube.com/watch?v=0_imbSU7mH4

Hope that helps!

Balavignesh