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Build Fuzzy Inference Systems Using Custom Functions in Fuzzy Logic Designer

When you build a fuzzy inference system, as described in Fuzzy Inference Process, you can replace the built-in membership functions, inference functions, or both with custom functions. In this section, you learn how to build a fuzzy inference system using custom functions in the Fuzzy Logic Designer app.

To build a fuzzy inference system using custom functions in the Fuzzy Logic Designer app:

Specify Custom Membership Functions

You can create custom membership functions and use them in the fuzzy inference process. The values of these functions must lie between 0 and 1. For more information on the properties of membership functions, see Membership Functions.

To create a custom membership function, and replace the built-in membership function:

You can also add a custom membership function to a FIS at the MATLAB command line. For example, to add custmf1 to the first input variable, input1 of the FIS, myFIS, and name it customMF1, type the following:

myFIS = addMF(myFIS,"input1","custmf1",[0 1 2 4 6 8 9 10],'Name',"customMF1");

Specify Custom Inference Functions

You can replace the built-in AND, OR, implication, aggregation, and defuzzification inference methods with custom functions. After you create the custom inference function, save it in your current working folder. To learn how to build fuzzy systems using custom inference functions, see the Build Fuzzy Inference Systems Using Custom Functions in Fuzzy Logic Designer section.

The guidelines for creating and specifying the functions for building fuzzy inference systems are described in the following sections.

• Create Custom AND and OR Functions

• Create Custom Implication Functions

• Create Custom Aggregation Functions

• Create Custom Defuzzification Functions

• Steps for Specifying Custom Inference Functions

x = [1 2 3 4];
min(x)

ans =
     1

x = [1 2 3 4;5 6 7 8;9 10 11 12];
min(x)

ans =
     1     2     3     4

a = [1 2; 3 4];
b = [2 2; 2 2];
min(a,b)

ans = 
    1     2
    2     2

function y = customimp(x1,x2)

if nargin == 1
    % x1 assumed to be non-empty column vector or matrix.    
    minVal = zeros(1,size(x1,2));
    y = ones(1,size(x1,2));    
 
    for i = 1:size(x1,1)
        y = max(minVal,sum([y;x1(i,:)])-1);
    end
else    
    % x1 and x2 assumed to be non-empty matrices.                  
    minVal = zeros(1,size(x1,2));
    y = zeros(size(x1));
  
    for i = 1:size(x1,1)
        y(i,:) = max(minVal,sum([x1(i,:);x2(i,:)])-1);
    end    
end

end

function y = customagg(x)

maxVal = ones(1,size(x,2));
y = zeros(1,size(x,2));

for i = 1:size(x,1)
    y = min(maxVal,sum([y;x(i,:)]));
end

end

function defuzzfun = customdefuzz(x,ymf)

total_area = sum(ymf);
defuzzfun = sum(ymf.*x)/total_area;

end

Specify Custom Type-Reduction Functions

For type-2 fuzzy inference systems, you can specify a custom type-reduction function. This function must be of the form y = customtr(x,umf,lmf), where x is the vector of values in the membership function input range. umf and lmf are the respective values of the upper and lower membership function for each x value. The output y is a two-element row vector of centroids [c_L,c_R].

For more information on type reduction, see Type-2 Fuzzy Inference Systems.

By default, type-2 Sugeno systems support only a weighted average form of type reduction. The following custom type-reduction function implements a weighted sum form of type reduction for a Sugeno system.

function y = customtr(x,umf,ymf)

y = zeros(1,2);

y(1) = sum(x.*umf);
y(2) = sum(x.*lmf);

end

To specify the custom type-reduction function for a FIS (myFIS) at the MATLAB command line, type

myFIS.DTypeReductionMethod = "customtr";

where customtr is the name of the custom defuzzification function.

Use Custom Functions in Code Generation

You can use custom functions in fuzzy inference systems for which you generate code. For more information on code generation for fuzzy systems, see Deploy Fuzzy Inference Systems.

If you use a nondouble data type for your generated code, you must propagate the data type from the input arguments of your custom function to the output argument. For example, the following custom aggregation function maintains the data type of x in y using the ones and zeros with the 'like' argument.

function y = customagg(x)

maxVal = ones(1,size(x,2),'like',x);
y = zeros(1,size(x,2),'like',x);

for i = 1:size(x,1)
    y = min(maxVal,sum([y;x(i,:)]));
end

end

For more information on writing functions that support C/C++ code generation, see MATLAB Programming for Code Generation (MATLAB Coder).