function

fuzzapp - Multi-Input Single Output Fuzzy Approximation of a Function.

Calling Sequence

fls=fuzzapp( order , domain_i , domain_o , partitions , f [,df] )

Parameters

• fls : fls structure.
• order : integer. 1 for first order, 2 for second order.
• domain_i : matrix of real with dimensions [ninputs,2] , were ninputs mean the number of inputs. Each row have two elements in the form [minDom maxDom] , where minDom meand the minimum value who take the input, and maxDom the maximum value.
• domain_o : row vector with two elements in the form [minDom maxDom] . minDom means the minimum value of the output, and maxDom the maximum value.
• partitions : column vector with the number or partitions for each input. partitions(j) is the number of partitions for the j input.
• f : function. The function to approximate. The result of f must be a scalar.This function must be vectorized, y=f(X) where X=[value1 , value2 , .... , value_ni] , ni=number of inputs
• df : function. The Jacobian of f. This function is required if order is equal to 2.

Description

fuzzapp create a Fuzzy Approximation for the function f .

Examples

// The function to approximate
deff("y=f(x)","y=sin(x)");
fls=fuzzapp(1,[-%pi %pi],[-1 1],10,f);
x=linspace(-%pi,%pi,100)';
Y_real=f(x);
Y_fuzz=evalfls(x,fls);
xbasc();
subplot(2,1,1);
plot2d(x,[Y_real Y_fuzz],leg="real@approximation");
xtitle("Fuzzy Approximation","x","y=f(x)");
subplot(2,1,2);
plot2d(x,abs(Y_real-Y_fuzz));
xtitle("Approximation Error","x","error");

Author

Jaime Urzua Grez