In this tutorial, we demonstrate how to compute the fuzzy integral in Mobius form with the k-additive integral.

First, clear your path and figures.

		  

close all; 
clear all;

Next, create 4 inputs, convert to Mobius representation and then run both forms and compare.

		  

% number of inputs
N = 4;

% binary encoding
% g = [ x1  x2  x12 x3  x13 x23 x123 x4  x14 x24 x124 x34 x134 x234 x1234 ]
FMbinary = [ 0.1 0.2 0.2 0.3 0.3 0.3 0.3  0.4 0.4 0.4 0.4  0.4 0.4  0.4  1 ];

% convert to Mobius
FMmobbinary = fi_convert_to_mobius(N, FMbinary);

%compute the FI
fi_choquet_integral_k_additive( [0.2 0.3 0.7 0.2] , FMmobbinary )
fi_choquet_integral_h_and_g_form( [0.2 0.3 0.7 0.2] , FMbinary )

The result is the following.

		  

ans =

    0.3500

ans =

    0.3500