Define Membership Functions Using Fuzzy Logic Designer

Since R2022b

Once you add a variable to your fuzzy inference system (FIS) using Fuzzy Logic Designer, you can define the membership functions (MFs) for that variable.

Add Membership Functions

To add membership functions to a given variable, select the variable in the System Browser or click the variable in the Fuzzy Inference System document. In the Property Editor, the app shows the input variable and membership function properties.

To add an MF, on the Design tab, in the Add Components gallery, click MF.

In the System Browser, the app adds an MF with a default configuration to the selected variable. You can view the properties of the MF in the table of the Property Editor.

You can also create a copy of an existing MF. To do so, in the System Browser, under the variable, right-click the membership function and select Add a copy.

The app creates a new MF with the same properties as the original MF and a modified name.

Distribute MFs Across Variable Range

Since R2023a

New MFs added to a variable have default properties. You can configure the values of these MFs manually. For more information, see Configure MFs.

You can also automatically distribute the existing MFs across the variable range. For example, the following figure shows three triangular membership function with the same default parameters.

To distribute these MFs across the variable range, click Evenly Distribute MFs.

View Membership Functions

To view a plot of the membership functions for a given variable, first select the variable in the System Browser. Then, open the Membership Function Editor document.

You can view the properties of the MFs in the Property Editor.

Configure MFs

You can edit the properties of an MF in the Property Editor. The types of MFs available for a variable and the MF properties depend on the type of FIS that you are designing.

Type-1 MFs

The following variables use type-1 MFs.

• Input and output variables of a type-1 Mamdani FIS

• Input variables of a type-1 Sugeno FIS

To configure a type-1 MF, specify the following properties.

• Name — Membership function name

• Type — Membership function type

• Parameters — Membership function parameters

You can specify the built-in type-1 MFs in the following table.

Type	Description	More Information
Generalized bell	Generalized bell-shaped membership function	gbellmf
Gaussian	Gaussian membership function	gaussmf
Two-sided Gaussian	Gaussian combination membership function	gauss2mf
Triangular	Triangular membership function	trimf
Trapezoidal	Trapezoidal membership function	trapmf
Linear S-shaped	Linear s-shaped saturation membership function	linsmf
Linear Z-shaped	Linear z-shaped saturation membership function	linzmf
Sigmoidal	Sigmoidal membership function	sigmf
Difference of sigmoids	Difference between two sigmoidal membership functions	dsigmf
Product of sigmoids	Product of two sigmoidal membership functions	psigmf
Z-shaped	Z-shaped membership function	zmf
Pi-shaped	Pi-shaped membership function	pimf
S-shaped	S-shaped membership function	smf

You can also specify custom MFs. For more information, see Build Fuzzy Systems Using Custom Functions.

Type-2 MFs

The following variables use type-2 MFs.

• Input and output variables of a type-2 Mamdani FIS

• Input variables of a type-2 Sugeno FIS

To configure a type-2 MF, specify the following properties.

• Name — Membership function name

• Type — Membership function type

• Upper Parameters — Upper membership function parameters

• Lower Scale — Lower membership function scale factor

• Lower Lag — Lower membership function delay factor, which defines the point at which the lower membership function value starts increasing from zero based on the value of the upper membership function. For example, a lag value of 0.1 indicates that the lower membership function becomes positive when the upper membership function has a membership value of 0.1.

A type-2 MF consists of a type-1 upper MF and a scaled lower MF. The Type and Upper Parameters properties define the upper MF and correspond to the Type and Parameters properties of a type-1 MF.

For more information on type-2 MFs, see Type-2 Fuzzy Inference Systems.

Sugeno Output MFs

For the output variables of type-1 and type-2 Sugeno systems, you can specify the following types of MFs.

• Constant — The location of the singleton MF in the output range is a constant value.

• Linear — The location of the singleton MF in the output range is a linear function of the input values.

For these membership functions, you can specify the following parameters.

• Name — Membership function name

• Type — Membership function type

• Parameters — Membership function parameters

For more information on Sugeno systems, see Sugeno Fuzzy Inference Systems.

Interactively Edit MFs

You can also interactively adjust the properties of a built-in type-1 or type-2 MF. To do so, in the Membership Function Editor, first click the MF. Then, you can modify the MF by dragging the control points.

Interactively editing a Sugeno output MF or a custom MF is not supported.

Delete MFs

To delete an MF from a variable, in the System Browser, under the variable, right-click the membership function and select Delete.

When you delete an MF from a variable, any rules that contain that variable are also deleted.