fismftype2

Interval type-2 fuzzy membership function

Description

Use a fismftype2 object to represent an interval type-2 fuzzy membership function (MF), which introduce additional uncertainty into a fuzzy inference system.

An interval type-2 membership function is represented by an upper and a lower membership function. The values of the upper membership function are always greater than or equal to the corresponding lower membership function values. The area enclosed by these membership functions is the footprint of uncertainty (FOU). For example, the following plot shows three type-2 membership functions for a given input variable.

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

Creation

Syntax

mf = fismftype2

mf = fismftype2(type,upperParameters)

mf = fismftype2(___,Name,Value)

Description

mf = fismftype2 creates a type-2 fuzzy membership function with default name, type, upper MF parameters, and lower MF configuration. To change the membership function properties, use dot notation.

mf = fismftype2(type,upperParameters) sets the Type and UpperParameters properties of the membership function.

mf = fismftype2(___,Name,Value) sets the Name, LowerScale, or LowerLag properties of the membership function using one or more name-value pair arguments for any of the other syntaxes.

Properties

Name — Membership function name

"mf" (default) | string | character vector

Membership function name, specified as a string or character vector.

Type — Membership function type

"trimf" (default) | string | character vector | function handle

Membership function type for both the upper and lower membership function, specified as a string or character vector that contains the name of a function in the current working folder or on the MATLAB^® path. You can also specify a handle to such a function. When you specify Type, you must also specify UpperParameters.

This table describes the values that you can specify for Type.

Membership Function Type	Description	For More Information
"gbellmf"	Generalized bell-shaped membership function	gbellmf
"gaussmf"	Gaussian membership function	gaussmf
"gauss2mf"	Gaussian combination membership function	gauss2mf
"trimf"	Triangular membership function	trimf
"trapmf"	Trapezoidal membership function	trapmf
"sigmf"	Sigmoidal membership function	sigmf
"dsigmf"	Difference between two sigmoidal membership functions	dsigmf
"psigmf"	Product of two sigmoidal membership functions	psigmf
"zmf"	Z-shaped membership function	zmf
"pimf"	Pi-shaped membership function	pimf
"smf"	S-shaped membership function	smf
String or character vector	Name of a custom membership function in the current working folder or on the MATLAB path. Custom output membership functions are not supported for Sugeno systems.	Build Fuzzy Systems Using Custom Functions
Function handle	Handle to a custom membership function in the current working folder or on the MATLAB path. Custom output membership functions are not supported for Sugeno systems.

Note

When you change Type using dot notation, the values in Parameters are automatically converted for the new membership function type.

UpperParameters — Upper membership function parameters

[0 0.5 1] (default) | vector

Upper membership function parameters, specified as a vector. The length of the parameter vector depends on the membership function type. When you specify Parameters, you must also specify Type.

LowerScale — Lower membership function scaling factor

1 (default) | positive scalar less than or equal to 1

Lower membership function scaling factor, specified as a positive scalar less than or equal to 1. Use LowerScale to define the maximum value of the lower membership function.

Depending on the value of LowerLag, the actual maximum lower membership function value can be less than LowerScale.

LowerLag — Lower membership function delay factor

scalar value between 0 and 1 | vector of length 2

Lower membership function delay factor, specified as a scalar value or a vector of length two. You can specify lag values between 0 and 1, inclusive.

The following membership function types support only a scalar LowerLag value:

• Symmetric MFs — gaussmf and gbellmf

• One-sided MFs — sigmf, smf, and zmf

All other built-in membership functions support either a scalar or vector LowerLag value. For these membership functions, when you specify a:

• Scalar value, the same lag value is used for both the left and right side of the membership function.

• Vector value, you can define different lag values for the left and right sides of the membership function.

The lag value 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.

By default, the lag value is 0.2. However, for some membership function types and upper membership function parameters, the software is unable to set a lower lag value to 0.2. In such a case, the default lag value is set to a different valid value..

When the lag value is zero, the lower membership function starts increasing at the same point as the upper membership function.

Some membership function types restrict the maximum lag value. For example, LowerLag must be less than 1 for the gaussmf, gauss2mf, gbellmf, sigmf, dsigmf, and psigmf membership functions.

Object Functions

evalmf

Evaluate fuzzy membership function

Examples

Create Type-2 Membership Function

Create type-2 membership function with default settings.

mf = fismftype2;

To modify the membership function settings, use dot notation. For example, specify a Gaussian upper membership function with a standard deviation of 2 and a mean of 10.

mf.Type = "gaussmf";
mf.UpperParameters = [2 10];

Specify the maximum lower membership function value as 0.8.

mf.LowerScale = 0.8;

Configure the lower membership function to start increasing when the upper membership function reaches 0.3.

mf.LowerLag = 0.3;

Create Type-2 Membership Function with Specified Upper MF Parameters

Create a trapezoidal type-2 membership function with specified upper MF parameters.

mf = fismftype2("trapmf",[3 4 6 7])

mf = 
  fismftype2 with properties:

               Type: "trapmf"
    UpperParameters: [3 4 6 7]
         LowerScale: 1
           LowerLag: [0.2000 0.2000]
               Name: "mf"

By default, the lower membership function has a maximum value of 1 and starts increasing when the upper MF is 0.2.

Configure Lower MF Parameters

Create a triangular type-2 membership function, specifying a maximum lower MF value of 0.9 and a membership function lag of 0.1.

mf = fismftype2("trimf",[1 2 3],'LowerScale',0.9,'LowerLag',0.1);