# How to get fuzzy output values instead of crisp output values?

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Hung on 4 Oct 2022
Commented: Hung on 5 Oct 2022
Hello,
I am following the fuzzy tool box designer example Build Fuzzy Systems Using Fuzzy Logic Designer - MATLAB & Simulink - MathWorks Nordic and have two questions:
1/ The tool showed the output result in crisp value after defuzzification, but are there ways to show the output in fuzzied values (0-1)?
2/ Are there ways to "look up" output value from 2 known input values from the 3D surface as mentioned in the video?
Thank you!

Sam Chak on 4 Oct 2022
The crisp out does not have an equivalent scalar fuzzy value. So, I think you probably mean finding the Aggregated output fuzzy set that the crisp value is calculated using the Centroid method. See Example below:
fis = mamfis('Name', "Fuzzy_Demo_2in1out")
fis =
mamfis with properties: Name: "Fuzzy_Demo_2in1out" AndMethod: "min" OrMethod: "max" ImplicationMethod: "min" AggregationMethod: "max" DefuzzificationMethod: "centroid" DisableStructuralChecks: 0 Inputs: [0×0 fisvar] Outputs: [0×0 fisvar] Rules: [0×0 fisrule] See 'getTunableSettings' method for parameter optimization.
% Fuzzy Input #1
fis = addInput(fis, [-1 1], 'Name', 'in1');
fis = addMF(fis, 'in1', 'gaussmf', [0.5 -1], 'Name', 'N');
fis = addMF(fis, 'in1', 'gaussmf', [0.5 1], 'Name', 'P');
% Fuzzy Input #2
fis = addInput(fis, [-1 1], 'Name', 'in2');
fis = addMF(fis, 'in2', 'gaussmf', [0.5 -1], 'Name', 'N');
fis = addMF(fis, 'in2', 'gaussmf', [0.5 1], 'Name', 'P');
cross = 0.125;
sigma = 0.5*(2.5 - 0)/sqrt(-2*log(cross));
% Fuzzy Output
fis = addOutput(fis, [-2.5 2.5], 'Name', 'out');
fis = addMF(fis, 'out', 'gaussmf', [sigma -2.5], 'Name', 'N');
fis = addMF(fis, 'out', 'gaussmf', [sigma 0.0], 'Name', 'Z');
fis = addMF(fis, 'out', 'gaussmf', [sigma 2.5], 'Name', 'P');
% Plot membership functions
figure(1)
subplot(2,1,1)
plotmf(fis, 'input', 1), grid on, title('in1 and in2')
subplot(2,1,2)
plotmf(fis, 'output', 1), grid on, title('U')
% Fuzzy Rules
rules = [...
"in1==N & in2==N => out=N"; ...
"in1==N & in2==P => out=Z"; ...
"in1==P & in2==N => out=Z"; ...
"in1==P & in2==P => out=P"; ...
];
% Generate output surface of MamFIS
figure(2)
opt = gensurfOptions('NumGridPoints', 41);
gensurf(fis, opt), title('Output Surface')
% Plot Aggregated output fuzzy set and Defuzzified output (Crisp value)
% find crisp output when in1 = -0.25 and in2 = -0.25
figure(3)
[output, fuzzifiedIn, ruleOut, aggregatedOut, ruleFiring] = evalfis(fis, [-0.25 -0.5])
output = -1.3279
fuzzifiedIn = 4×2
0.3247 0.6065 0.3247 0.0111 0.0439 0.6065 0.0439 0.0111
ruleOut = 101×4
0.3247 0.0002 0.0002 0.0000 0.3247 0.0003 0.0003 0.0000 0.3247 0.0005 0.0005 0.0000 0.3247 0.0006 0.0006 0.0000 0.3247 0.0009 0.0009 0.0000 0.3247 0.0012 0.0012 0.0000 0.3247 0.0016 0.0016 0.0000 0.3247 0.0021 0.0021 0.0000 0.3247 0.0028 0.0028 0.0000 0.3247 0.0037 0.0037 0.0000
aggregatedOut = 101×1
0.3247 0.3247 0.3247 0.3247 0.3247 0.3247 0.3247 0.3247 0.3247 0.3247
ruleFiring = 4×1
0.3247 0.0111 0.0439 0.0111
outputRange = linspace(fis.output.range(1), fis.output.range(2), length(aggregatedOut))';
plot(outputRange, aggregatedOut, [output output], [0 1]), grid on
xlabel('output')
ylabel('Output Membership')
legend('Aggregated output fuzzy set', 'Defuzzified output')
The blue curve is the Aggregated output fuzzy set. The vertical red line marks the Defuzzified output that is computed from the Centroid Defuzzification method.
Hung on 5 Oct 2022
@Sam Chak Thank you very much. I understand now :-)
Good day!

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