fistree

Network of connected fuzzy inference systems

Description

Use a fistree object to represent a tree of interconnected fuzzy inference systems.

Creation

Syntax

fisTree = fistree(fis,connections)

fisTree = fistree(___,Name,Value)

Description

fisTree = fistree(fis,connections) creates a network of interconnected fuzzy inference system objects, setting its FIS and Connections properties

fisTree = fistree(___,Name,Value) sets the Name or DisableStructuralChecks property of the FIS tree using name-value arguments. Specify these arguments after the arguments described in the previous syntax. For example, fistree(__,'Name',"mytree") sets the name of the FIS tree to "mytree". You can specify both properties using two name-value arguments.

Properties

Name — FIS tree name

"fistreemodel" (default) | string | character vector

FIS tree name, specified as a string or character vector.

FIS — Fuzzy inference systems

array

This property is read-only.

Fuzzy inference systems, specified as an array of FIS objects. You can specify any combination of mamfis, sugfis, mamfistype2, and sugfistype2 objects. Each fuzzy inference system in the fis array must have at least one input and one output for fistree construction. To evaluate a fistree, each fuzzy inference system must have at least one rule.

Connections — Connections between fuzzy inference systems

two-column string array

Connections between fuzzy inference systems, specified as a two-column string array. Each row represents a connection between two FIS objects. You can specify two types of connections.

1. Output-to-input connections — Specify a connection from the output of one FIS to the input of a different FIS.

2. Input-to-input connections — Specify a connection between two inputs so that they use the same input value.

To define a connection, specify the FIS name and variable name for both the source a destination of the connection. For example, ["fisFrom/out1" "fisTo/in1"] defines a connection from output out1 of FIS fisFrom to input in1 of FIS fisTo.

The following figure demonstrates the different connection types using three FIS objects, fis1, fis2, and fis3.

This FIS tree includes the following connections.

• ["fis1/output1" "fis3/input1"] — Connection from output output1 of fis1 to input input1 of fis3

• ["fis2/output1" "fis3/input2"] — Connection from output output1 of fis2 to input input2 of fis3

• ["fis1/input2" "fis2/input1"] — Connection from input input2 of fis1 to input input1 of fis2

Connections must satisfy the following conditions:

1. A fistree object must have at least one FIS input without any incoming connection and one FIS output without any outgoing connection.

2. A FIS input cannot have more than one incoming connection.

3. A FIS output can have more than one outgoing connection.

4. An input and output of the same FIS cannot be connected. In other words, you cannot create loops between connected FIS objects.

5. Symmetric connections between two inputs are not supported, For example, ["fis1/a" "fis2/b";"fis2/b" "fis1/a"] is not supported. Instead, specify ["fis1/a" "fis2/b"] or ["fis2/b" "fis1/a"].

6. Self-input loops, such as ["fis1/a" "fis1/a"], are not supported.

Inputs — Inputs to FIS tree

string array

This property is read-only.

Inputs to the FIS tree, specified as an array of strings. Inputs are automatically determined using the specified connections of the fistree object. FIS inputs with no incoming connections are included in Inputs.

Update this property by updating the connections of the fistree object.

Outputs — Outputs of FIS tree

string array

Outputs of the FIS tree, specified as a string array. Outputs are automatically determined using the specified connections of the fistree object. FIS outputs without any outgoing connections are included in Outputs.

You can update this property after initial construction of the fistree object. You can remove an existing input or add additional intermediate outputs. Outputs must contain at least one output.

DisableStructuralChecks — Option for disabling structural checks

false (default) | true

Option for disabling structural checks when the FIS tree is updated after initial FIS creation, specified as one of the following values.

• false — Automatically update connections, inputs, and outputs. This option ensures that the FIS tree is always valid and can be evaluated.

• true — Do not automatically update connections, inputs, and outputs. In this case, the resulting FIS tree can be in an invalid state, which can cause an error during evaluation.

Enable this option to improve computational efficiency when you programmatically construct a FIS tree.

Object Functions

evalfis	Evaluate fuzzy inference system
plotfis	Display fuzzy inference system
getTunableSettings	Obtain tunable settings from fuzzy inference system
getTunableValues	Obtain values of tunable parameters from fuzzy inference system
setTunableValues	Specify tunable parameter values of a fuzzy inference system

Examples

Create Tree of Connected Fuzzy Inference Systems

Create a Mamdani fuzzy inference system and a Sugeno fuzzy inference system.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis2 = sugfis('Name','fis2','NumInputs',2,'NumOutputs',1);

Define a connection from the output of fis1 to the first input of fis2.

con1 = ["fis1/output1" "fis2/input1"];

Create a FIS tree using the fuzzy inference systems and connection.

tree = fistree([fis1 fis2],con1);

Visualize the tree.

plotfis(tree)

Update Fuzzy Inference Systems in FIS Tree

Create a tree with two FISs and no connections.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);

fisT = fistree([fis1 fis2],[]);

Display the FIS tree configuration.

plotfis(fisT)

You can add a FIS to a FIS tree by appending a FIS object to the FIS property of the tree.

Add fis3 to the FIS tree.

fis3 = mamfis('Name','fis3','NumInputs',2,'NumOutputs',1);
fisT.FIS(end+1) = fis3;

Connect the outputs of fis1 and fis2 to the inputs of fis3.

fisT.Connections = [
    "fis1/output1" "fis3/input1";
    "fis2/output1" "fis3/input2"];

Display the updated FIS tree configuration.

plotfis(fisT)

Remove the first FIS (fis1) from the FIS tree.

fisT.FIS(1) = [];

Display the updated FIS tree configuration.

plotfis(fisT)

The corresponding connection to the first input of fis3 is also removed.

Use Same Value for Multiple Inputs of FIS Tree

Create fis1, fis2, and fis3, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);
fis3 = mamfis('Name','fis3','NumInputs',2,'NumOutputs',1);

Create a connection between output 1 of fis1 and input 1 of fis3.

con1 = ["fis1/output1" "fis3/input1"];

Create a connection between output 1 of fis2 and input 2 of fis3.

con2 = ["fis2/output1" "fis3/input2"];

Create a connection between input 2 of fis1 and input 1 of fis2.

con3 = ["fis1/input2" "fis2/input1"];

Create and display the FIS tree.

fuzzTree = fistree([fis1 fis2 fis3],[con1;con2;con3]);
plotfis(fuzzTree)

Display the inputs of the FIS tree. These inputs correspond to all free inputs that do not have an incoming connection.

fuzzTree.Inputs

ans = 3×1 string
    "fis1/input1"
    "fis1/input2"
    "fis2/input2"

Evaluate the fuzzy tree. Specify values for input 1 of fis1, input 2 of fis1, and input 2 of fis2. The value for input 2 of fis1 is also applied to input 1 of fis2.

output = evalfis(fuzzTree,[0.8 0.25 0.7]);

Update FIS Tree Outputs

Create two FIS objects, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);

Connect the output of fis1 to the second input of fis2.

con = ["fis1/output1" "fis2/input2"];

Create the FIS tree.

fuzzTree = fistree([fis1 fis2],con);

Display outputs of the FIS tree. By default, the open FIS output from fis2 is an output of the FIS tree.

fuzzTree.Outputs

ans = 
"fis2/output1"

Visualize the FIS tree.

plotfis(fuzzTree,Legend="on")

Add the output of fis1 to the list of outputs.

fuzzTree.Outputs(end+1) = "fis1/output1";

Display the updated output list of the FIS tree.

fuzzTree.Outputs

ans = 2×1 string
    "fis2/output1"
    "fis1/output1"

Visualize the FIS tree. The added intermediate output is highlighted.

plotfis(fuzzTree,Legend="on")

Evaluate the FIS tree. The result contains the outputs from fis2 and fis1.

evalfis(fuzzTree,[0.5 0.2 0.8])

ans = 1×2

    0.1579    0.1579

Remove the first output from the list.

fuzzTree.Outputs(1) = [];

Display the updated output list of the FIS tree.

fuzzTree.Outputs

ans = 
"fis1/output1"

Visualize the FIS tree without the removed output. The visualization indicates that the output of fis2 is unused.

plotfis(fuzzTree,Legend="on")

Evaluate the FIS tree again. The result now contains the output of only fis2.

evalfis(fuzzTree,[0.5 0.2 0.8])

ans = 0.1579

Create Incremental FIS Tree

This example shows the construction of an incremental FIS tree. For more information on the types of fuzzy tree structures, see Fuzzy Trees.

Create fuzzy systems fis1, fis2, and fis3, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis1.Inputs(1).Name = "color";
fis1.Inputs(2).Name = "doors";
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);
fis2.Inputs(2).Name = "power";
fis3 = mamfis('Name','fis3','NumInputs',2,'NumOutputs',1);
fis3.Inputs(2).Name = "autopilot";
fis3.Outputs(1).Name = "prediction";

Create a connection between output 1 of fis1 and input 1 of fis2.

con1 = ["fis1/output1" "fis2/input1"];

Create a connection between output 1 of fis2 and input 1 of fis3.

con2 = ["fis2/output1" "fis3/input1"];

Create the FIS tree.

incTree = fistree([fis1 fis2 fis3],[con1;con2]);

Visualize the tree structure. At each level of the tree structure, an additional input is combined with the output of the previous level.

plotfis(incTree)

Create Aggregated FIS Tree

This example shows the construction of an aggregated FIS tree. For more information on the types of fuzzy tree structures, see Fuzzy Trees.

Create fuzzy systems fis1, fis2, and fis3, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis1.Inputs(1).Name = "dist_obs";
fis1.Inputs(2).Name = "angle_obs";
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);
fis2.Inputs(1).Name = "dist_tar";
fis2.Inputs(2).Name = "angle_tar";
fis3 = mamfis('Name','fis3','NumInputs',2,'NumOutputs',1);
fis3.Outputs(1).Name = "heading_robot";

Create a connection between output 1 of fis1 and input 1 of fis3.

con1 = ["fis1/output1" "fis3/input1"];

Create a connection between output 1 of fis2 and input 2 of fis3.

con2 = ["fis2/output1" "fis3/input2"];

Create the FIS tree.

aggTree = fistree([fis1 fis2 fis3],[con1;con2]);

Visualize the tree structure.

plotfis(aggTree)

Create Cascaded FIS Tree

This example shows the construction of a cascaded FIS tree. For more information on the types of fuzzy tree structures, see Fuzzy Trees.

Create fuzzy systems fis1, fis2, fis3, and fis4, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis1.Inputs(1).Name = "dist_obs";
fis1.Inputs(2).Name = "angle_obs";
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);
fis2.Inputs(1).Name = "dist_tar";
fis2.Inputs(2).Name = "angle_tar";
fis3 = mamfis('Name','fis3','NumInputs',2,'NumOutputs',1);
fis4 = mamfis('Name','fis4','NumInputs',2,'NumOutputs',1);
fis4.Inputs(2).Name = "preheading_robot";
fis4.Outputs(1).Name = "heading_robot";

Create a connection between output 1 of fis1 and input 1 of fis3.

con1 = ["fis1/output1" "fis3/input1"];

Create a connection between output 1 of fis2 and input 2 of fis3.

con2 = ["fis2/output1" "fis3/input2"];

Create a connection between output 1 of fis3 and input 1 of fis4.

con3 = ["fis3/output1" "fis4/input1"];

Create the FIS tree.

casTree = fistree([fis1 fis2 fis3 fis4],[con1;con2;con3]);

Visualize the tree structure.

plotfis(casTree)

Create and Evaluate Parallel FIS Tree

This example shows the construction of a parallel FIS tree. For more information on the types of fuzzy tree structures, see Fuzzy Trees.

Create fuzzy systems fis1, fis2, and fis3, each with two inputs and one output.

fis1 = mamfis('Name','fis1','NumInputs',2,'NumOutputs',1);
fis2 = mamfis('Name','fis2','NumInputs',2,'NumOutputs',1);

Create the FIS tree such that the FIS objects are in parallel; that is, the tree contains no interconnections and all the FIS outputs are FIS tree outputs.

parTree = fistree([fis1 fis2],[]);

Visualize the tree.

plotfis(parTree)

Evaluate the FIS tree.

output = evalfis(parTree,[0.1 0.3 0.8 0.4]);

Generate the final output by summing the FIS tree outputs.

finalOutput = sum(output);