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In this tutorial, we highlight the Shapley and interaction index.

First, clear your path and figures.

```
``````
close all;
clear all;
```

Next, lets make the ChI become the minimum operator.

```
``````
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OWA and min
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[g] = fi_owa( [ 0 0 1 ] )'
[ ShapleyVector ] = fi_shapley( g )
[InteractionIndex] = fi_interaction_index( g )
```

The result is the following (see below). Note, the Shapley values are equal, which is true for any OWA/LCOS.

```
``````
g =
0 0 0 0 0 0 1
ShapleyVector =
0.3333 0.3333 0.3333
InteractionIndex =
1.0000 0.5000 0.5000
0.5000 1.0000 0.5000
0.5000 0.5000 1.0000
```

Next, lets make the ChI become the maximum operator.

```
``````
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OWA and max
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[g] = fi_owa( [ 1 0 0 ] )'
[ ShapleyVector ] = fi_shapley( g )
[InteractionIndex] = fi_interaction_index( g )
```

The result is the following (see below). Note, the Shapley values are again equal, which is true for any OWA/LCOS.

```
``````
g =
1 1 1 1 1 1 1
ShapleyVector =
0.3333 0.3333 0.3333
InteractionIndex =
1.0000 -0.5000 -0.5000
-0.5000 1.0000 -0.5000
-0.5000 -0.5000 1.0000
```

Next, lets make the ChI become the average operator.

```
``````
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OWA and average
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[g] = fi_owa( [ 1 1 1 ] ./ 3 )'
[ ShapleyVector ] = fi_shapley( g )
[InteractionIndex] = fi_interaction_index( g )
```

The result is the following (see below). Note, the Shapley values are again equal, which is true for any OWA/LCOS. Furthermore, the off diagional interaction terms are 0, which is true for additivity.

```
``````
g =
Columns 1 through 5
0.3333 0.3333 0.6667 0.3333 0.6667
Columns 6 through 7
0.6667 1.0000
ShapleyVector =
0.3333 0.3333 0.3333
InteractionIndex =
1.0000 0.0000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.0000
```

Last, we do a Sugeno lambda fuzzy measure example.

```
``````
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Sugeno lambda FM-based
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[g, lambda] = fi_sugeno_lambda_measure( [0.2 0.3 0.1] )
[ ShapleyVector ] = fi_shapley( g )
[InteractionIndex] = fi_interaction_index( g )
```

The result is the following (see below).

```
``````
g =
Columns 1 through 5
0.2000 0.3000 0.6865 0.1000 0.3622
Columns 6 through 7
0.4933 1.0000
lambda =
3.1091
ShapleyVector =
0.3437 0.4592 0.1971
InteractionIndex =
1.0000 0.2155 0.0912
0.2155 1.0000 0.1223
0.0912 0.1223 1.0000
```