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Convert type-1 fuzzy inference system into type-2 fuzzy inference system

Since R2019b



fisT2 = convertToType2(fisT1) converts the type-1 fuzzy inference system fisT1 into a type-2 fuzzy inference system fisT2.


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Create a type-1 fuzzy inference system. For this example, load the tipper.fis file.

fisT1 = readfis('tipper');

View the membership function for the first input variable.


Figure contains an axes object. The axes object with xlabel service, ylabel Degree of membership contains 6 objects of type line, text.

Convert fisT1 into a type-2 fuzzy inference system.

fisT2 = convertToType2(fisT1);

View the converted membership functions for the first input variable.


Figure contains an axes object. The axes object with title Footprint of uncertainty (FOU), xlabel service, ylabel Degree of membership contains 12 objects of type line, patch, text. These objects represent UpperMF, LowerMF, FOU.

To create a type-2 FIS from input/output data, you must first create a type-1 FIS using genfis.

Load training data and generate a FIS using subtractive clustering.

load clusterDemo.dat
inputData = clusterDemo(:,1:2);
outputData = clusterDemo(:,3);
opt = genfisOptions('SubtractiveClustering',...
                    'ClusterInfluenceRange',[0.5 0.25 0.3]);
fisT1 = genfis(inputData,outputData,opt);
ans = 
  fisvar with properties:

                   Name: "out1"
                  Range: [-0.1274 1.1458]
    MembershipFunctions: [1x3 fismf]

Convert the generated FIS to a type-2 FIS.

fisT2 = convertToType2(fisT1);

Since the initial type-1 FIS is a Sugeno system, only the input MFs are converted to type-2 MFs.

Input Arguments

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Type-1 fuzzy inference system, specified as a mamfis or sugfis object.

Output Arguments

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Type-2 fuzzy inference system, returned as one of the following:

The properties of fisT2 match the corresponding properties of fisT1, except that each type-1 membership function (except for Sugeno output membership functions) is converted to a type-2 membership function. The upper membership function parameters of each type-2 membership function in fisT2 match the membership function parameters of the corresponding type-1 membership function in fisT1.

fisT2 has default LowerScale and LowerLag values and uses the default "karnikmendel" type reduction method.

Alternative Functionality


You can interactively convert a type-1 FIS into a type-2 FIS using the Fuzzy Logic Designer app. You can then export the system to the MATLAB® workspace.

Version History

Introduced in R2019b