How to design a Fuzzy System for only five data points

I'm new to Matlab. I want to make membership function of an array (Normalized Delay) having 5 values in it . x-axis -> Norm Delay, Y-axis-> Membership function from 0 to 1. Anyone can guide me Please how to make rules? What is the fuzzificaton language? How to implement it in Matlab? Thankyou.

[Sam Chak]

Hi @M Ali Naqvi

It is perfect okay to ask and learn how to do it in MATLAB.

Can you at least sketch how the membership functions should look like on a piece of paper, then snap a picture and insert the image here by clicking the Image button ?

Answer 1

[Sam Chak]

Hi @M Ali Naqvi

Here is a demonstration of employing the Stone–Weierstrass theorem (instead of Taylor series) to design a relatively simple fuzzy system aimed at achieving 100% accuracy in the prediction of the five data points.

%% 5-point Data
x   = 1:5;
y   = randn(1, 5)

y = 1×5

0.8022 -1.6507 0.4491 -0.5216 0.5675

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figure
plot(x, y, '-o'), grid on
xlabel('x (input)')
ylabel('y (output)')
title('5-point Data')

%% Sugeno Fuzzy System
fis = sugfis;

% Fuzzy Input 1
fis = addInput(fis, [x(1) x(end)], 'Name', 'X');
fis = addMF(fis, 'X', 'linzmf', [      x(1), x(2)], 'Name', 'x1');
fis = addMF(fis, 'X',  'trimf', [x(1), x(2), x(3)], 'Name', 'x2');
fis = addMF(fis, 'X',  'trimf', [x(2), x(3), x(4)], 'Name', 'x3');
fis = addMF(fis, 'X',  'trimf', [x(3), x(4), x(5)], 'Name', 'x4');
fis = addMF(fis, 'X', 'linsmf', [x(4), x(5)      ], 'Name', 'x5');

plotmf(fis, 'input', 1), grid on, 
title('Uniformly distributed membership functions of Input x')

●

% Fuzzy Output
fis = addOutput(fis,  [min(y) max(y)], 'Name', 'Y');
fis = addMF(fis, 'Y', 'constant', y(1), 'Name', 'y1');
fis = addMF(fis, 'Y', 'constant', y(2), 'Name', 'y2');
fis = addMF(fis, 'Y', 'constant', y(3), 'Name', 'y3');
fis = addMF(fis, 'Y', 'constant', y(4), 'Name', 'y4');
fis = addMF(fis, 'Y', 'constant', y(5), 'Name', 'y5');

% Fuzzy Rules
rules = [
    "X==x1 => Y=y1"
    "X==x2 => Y=y2"
    "X==x3 => Y=y3"
    "X==x4 => Y=y4"
    "X==x5 => Y=y5"
    ];
fis = addRule(fis, rules);

%% Fuzzy model
figure
opt = gensurfOptions('NumGridPoints', 5);
gensurf(fis, opt);
title('Achieving 100% prediction accuracy in Fuzzy Model')