Load Example Data

This example trains a FIS using automobile fuel consumption data. The goal is for the FIS to predict fuel consumption in miles per gallon (MPG) using several automobile profile attributes. The training data is available in the University of California at Irvine Machine Learning Repository and contains data collected from automobiles of various makes and models.

This example uses the following six input data attributes to predict the output data attribute MPG with a FIS:

Load the data. Each row of the data set obtained from the repository represents a different automobile profile.

[data,name] = loadGasData;

data contains seven columns, where the first six columns contain the input attribute values. The final column contains the predicted MPG output. Split data into input and output data sets, X and Y, respectively.

X = data(:,1:6);
Y = data(:,7);

Partition the input and output data sets into training data (odd-indexed samples) and validation data (even-indexed samples).

trnX = X(1:2:end,:); % Training input data set
trnY = Y(1:2:end,:); % Training output data set
vldX = X(2:2:end,:); % Validation input data set
vldY = Y(2:2:end,:); % Validation output data set

The FIS tree structure that you create in this example uses a different input order than the original data. Rearrange the training and validation input data to use the new order.

inputOrders1 = [4 6 2 5 3 1];
trnX = trnX(:,inputOrders1);
vldX = vldX(:,inputOrders1);

load mpgInitialFISTree

Define Initial FIS Tree Structure

The first step of the tuning process is to define the initial structure of your FIS tree. To define this structure, specify:

To create your FIS in the app, you can:

For this example, open Fuzzy Logic Designer and import the mpgInitialFISTree system from the MATLAB^® workspace.

fuzzyLogicDesigner(mpgInitialFISTree)

Import Training Data

To select input and output data for tuning, on the Tuning tab:

Tune FIS Tree

Tuning is performed in two steps.

The first step is less computationally expensive due to the small number of rule parameters, and it quickly converges to a fuzzy rule base during training. In the second step, using the rule base from the first step as an initial condition provides fast convergence of the parameter tuning process.

Analyze Intermediate Data

To gain insight into the operation of your FIS tree, you can add the outputs of the component FIS objects as outputs of your FIS tree. For this example, examine how the outputs of fis1, fis2, and fis3 correlate with the output validation data.

First, since you are analyzing the behavior of fistree_tuned, remove the fistree_learned output from the System Validation plots. To do so, in the Design Browser, clear the entry in the Compare column for fis_learned.

To compare FIS tree outputs with validation data, the number of FIS tree outputs must match the number of outputs in the validation output data, which for this example is one. To configure the FIS tree outputs, in the System Browser, under fistree_tuned, click Outputs.

To make the output of fis1 the only output of the FIS tree, in the Property Editor:

Click Apply.

In the System Validation document, clear the Prediction errors checkbox.

Repeat this process to view the output behavior for fis2.

Repeat this process to view the output behavior for fis3.

The outputs of fis1, fis2, and fis3 all correlate with the output validation data. The correlation of fis1 appears to be strongest, followed by fis3.

To validate this analysis, you can export the system validation simulation results to the MATLAB workspace for further analysis. For more information on exporting simulation results, see Export FIS and Simulation Data from Fuzzy Logic Designer. For an example correlation analysis, see the command-line tuning example Tune FIS Tree at the Command Line

After analyzing the intermediate outputs, reset the FIS output configuration. In the Property Editor enable the output fis5 as a FIS tree output and clear the Intermediate Output value the connected outputs.

Simplify and Retrain FIS Tree

For this example, to see if you can get comparable performance for a simplified FIS tree, remove fis2 and fis4 from the original FIS structure and retune the FIS tree.

To do so, first open a new instance of Fuzzy Logic Designer with the original FIS tree structure. On the Design tab, under Import > Import Fuzzy Inference System from Workspace, select mpgInitialFISTree.

To remove fis2, in the System Browser, under FIS, right-click fis2 and select Delete. When you delete a FIS object from your FIS tree, any connections to that FIS object are also removed.

Similarly, remove fis4.

Connect the output of fis1 to the first input of fis5.

The following figure shows the resulting FIS tree configuration.

To learn rules, disable parameter tuning for fis1, fis3, and fis5. In the System Browser, under FIS, select each FIS individually and, in the Tunable Parameters pane, click Tune None for both the input and output tables.

On the Tuning tab, select the simplified four-input training data:

Click Tuning Options. In the Tuning Options dialog box, configure the same rule-learning options that you used previously, as shown in the following figure.

Click Tune.

The RMSE for this learning step is 3.368, which is similar to the result from the original rule learning step.

Accept the training result and rename the resulting FIS tree design to mpgsimple_learned.

To tune the rule and MF parameters, configure the same parameter-tuning options that you used previously, as shown in the following figure.

Click Tune.

The RMSE for this learning step is 2.868, which is lower than the result from the original rule learning step.

Accept the training result and rename the resulting FIS tree design to mpgsimple_tuned.

To validate the final tuned system, first select the Compare checkbox for the mpgsimple_tuned system in the Design Browser, and clear the Compare checkbox for all the other designs.

On the Design tab:

Open the System Validation document.

The RMSE for the validation data is 3.014, which is similar to the result from the original rule learning step.

Export Tuned FIS Tree

To save your FIS tree for further analysis and development, you can either export it to the MATLAB workspace or save it to a FIS file. For this example, export both the simplified tuned FIS tree to the MATLAB workspace.

On the Design tab, under Export, select Export Fuzzy Inference System to Workspace.

In the Export Fuzzy Inference System to Workspace dialog box, in the Export column, select the checkbox for mpgsimple_tuned.

Click Export.