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:');
disp(rankIndex);
% 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:');
disp(rankIndex);
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
