addMF

Add membership function to fuzzy variable

Syntax

fisOut = addMF(fisIn,varName)

fisOut = addMF(fisIn,varName,type,parameters)

fisOut = addMF(___,Name,Value)

varOut = addMF(varIn)

varOut = addMF(varIn,type,parameters)

varOut = addMF(___,Name,Value)

Description

fisOut = addMF(fisIn,varName) adds a default membership function to the input or output variable varName in the fuzzy inference system fisIn and returns the resulting fuzzy system in fisOut.

fisOut = addMF(fisIn,varName,type,parameters) adds a membership function with the specified type and parameters.

fisOut = addMF(___,Name,Value) configures the membership function using one or more name-value pair arguments.

varOut = addMF(varIn) adds a default membership function to fuzzy variable varIn and returns the resulting fuzzy variable in varOut.

If varIn does not contain any membership functions, this syntax adds a default type-1 membership function. Otherwise, the type of the added membership function matches the type of the existing membership functions in varIn.

varOut = addMF(varIn,type,parameters) adds a membership function with the specified type and parameters.

varOut = addMF(___,Name,Value) specifies the name of the membership function using the Name name-value argument.

To add a type-2 membership function to a fuzzy variable with no existing membership functions, you must specify either the LowerLag or LowerScale name-value argument.

Examples

Add Membership Function to Fuzzy Inference System

Create a Mamdani fuzzy system, and add three input variables and one output variable. For this example, give the second input variable and the output variable the same name.

fis = mamfis;
fis = addInput(fis,[0 80],"Name","speed");
fis = addInput(fis,[0 100],"Name","throttle");
fis = addInput(fis,[0 10],"Name","distance");
fis = addOutput(fis,[0 100],"Name","throttle");

Add a membership function to the first input variable, specifying a trapezoidal membership function, and set the membership function parameters.

fis = addMF(fis,"speed","trapmf",[-5 0 10 30]);

You can also specify the name of your membership when you add it to a fuzzy system. Add a membership function called "high" to the first input variable.

fis = addMF(fis,"speed","trapmf",[50 70 80 85],'Name',"high");

View the membership functions for the first input variable.

plotmf(fis,"input",1)

If your system has an input variable with the same name as an output variable, you must specify the variable type when adding a membership function. For example, add a membership function to the output variable.

fis = addMF(fis,"throttle","trimf",[0 20 40],'VariableType',"output");
plotmf(fis,"output",1)

Alternatively, you can add a default membership function to a fuzzy system and set its parameters using dot notation. For example, add and configure a membership function for the third input variable.

fis = addMF(fis,"distance");
fis.Inputs(3).MembershipFunctions(1).Type = "trapmf";
fis.Inputs(3).MembershipFunctions(1).Parameters = [-1 0 2 4];
plotmf(fis,"input",3)

Add Membership Function to Type-2 Fuzzy Inference System

Create a type-2 Sugeno fuzzy system, and add two input variables and one output variable.

fis = sugfistype2;
fis = addInput(fis,[0 80],"Name","speed");
fis = addInput(fis,[0 10],"Name","distance");
fis = addOutput(fis,[0 100],"Name","braking");

Add a membership function to the first input variable, specifying a trapezoidal membership function, and set the membership function parameters. This type-2 membership function uses default lower membership function lag and scale parameters.

fis = addMF(fis,"speed","trapmf",[-5 0 10 30]);

You can also specify the configuration of the lower MF when adding a type-2 membership function.

fis = addMF(fis,"speed","trapmf",[10 30 50 70],'LowerScale',0.8,'LowerLag',0.1);

You can also specify the name of your membership function when you add it to a fuzzy system. Add a membership function called "high" to the first input variable.

fis = addMF(fis,"speed","trapmf",[50 70 80 85],'Name',"high");

View the membership functions for the first input variable.

plotmf(fis,"input",1)

Add Membership Function to Fuzzy Variable

Create a fuzzy variable with a specified range.

var = fisvar([0 1]);

Add a membership function to the variable, specifying a trapezoidal membership function, and set the membership function parameters.

var = addMF(var,"trapmf",[-0.5 0 0.2 0.4]);

You can also specify the name of your membership when you add it to a fuzzy variable. For example, add a membership function called "large".

var = addMF(var,"trapmf",[0.6 0.8 1 1.5],'Name',"large");

View the membership functions.

var.MembershipFunctions

ans = 
  1x2 fismf array with properties:

    Type
    Parameters
    Name

  Details:
          Name        Type               Parameters         
         _______    ________    ____________________________

    1    "mf1"      "trapmf"    -0.5       0     0.2     0.4
    2    "large"    "trapmf"     0.6     0.8       1     1.5

Alternatively, you can add a default membership function to a fuzzy variable and set its parameters using dot notation.

var = fisvar([0 1]);
var = addMF(var);
var.MembershipFunctions(1).Type = "trapmf";
var.MembershipFunctions(1).Parameters = [-0.5 0 0.2 0.4];

Add Type-2 Membership Function to Fuzzy Variable

Create a fuzzy variable with a specified range. By default, this variable has no membership functions.

var = fisvar([0 9]);

To add a type-2 membership function to a variable with no existing membership functions, specify either a LowerLag or LowerScale value for the membership function. For example specify a lower scale value.

var = addMF(var,"trimf",[0 3 6],'LowerScale',1);

Once a variable contains a type-2 membership function, you can add additional type-2 membership functions without specifying one of these parameters.

var = addMF(var,"trimf",[3 6 9]);

View the membership functions.

var.MembershipFunctions

ans = 
  1x2 fismftype2 array with properties:

    Type
    UpperParameters
    LowerScale
    LowerLag
    Name

  Details:
         Name      Type      Upper Parameters    Lower Scale    Lower Lag 
         _____    _______    ________________    ___________    __________

    1    "mf1"    "trimf"      0    3    6            1         0.2    0.2
    2    "mf2"    "trimf"      3    6    9            1         0.2    0.2

Specify Custom Membership Functions at Command Line

To use a custom membership function when designing a FIS at the MATLAB® command line, specify the name and parameters when adding the membership function using addMF. For example, the following command adds custom membership function custmf1 to the first input variable, input1, of FIS myFIS and names it customMF1.

Create a FIS and add an input variable.

myFIS = mamfis;
myFIS = addInput(myFIS);

Add custom membership function custmf1 to the first input variable, input1, of this FIS and name it customMF1.

myFIS = addMF(myFIS,"input1","custmf1",[0 1 2 4 6 8 9 10],...
    "Name","customMF1");

Ensure that the range of the input variable matches the expected range of your membership function. For this example, set the range of the first input to [0 10].

myFIS.Inputs(1).Range = [0 10];

To verify the appearance of your membership function, you can plot it using plotMF.

plotmf(myFIS,"input",1) 

Input Arguments

fisIn — Fuzzy inference system

mamfis object | sugfis object | mamfistype2 object | sugfistype2 object

Fuzzy inference system, specified as one of the following:

• mamfis object — Mamdani fuzzy inference system

• sugfis object — Sugeno fuzzy inference system

• mamfistype2 object — Type-2 Mamdani fuzzy inference system (since R2019b)

• sugfistype2 object — Type-2 Sugeno fuzzy inference system (since R2019b)

varName — Variable name

string | character vector

Variable name, specified as a string or character vector. You can specify the name of either an input or output variable in your FIS. If your system has an input variable with the same name as an output variable, specify the type of the variable you want to add a membership function to using the VariableType name-value pair.

type — Membership function type

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

Membership function type, 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 parameters.

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
"linsmf"	Linear s-shaped saturation membership function (since R2022a)	linsmf
"linzmf"	Linear z-shaped saturation membership function (since R2022a)	linzmf
"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
"constant"	Constant membership function for Sugeno output membership functions	Sugeno Fuzzy Inference Systems
"linear"	Linear membership function for Sugeno output membership functions
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.

parameters — Membership function parameters

[0 0.5 1] (default) | vector

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.

When fisIn is a type-1 FIS or varIn contains type-1 membership functions, parameters sets the Parameters property of the added membership function.

When fisIn is a type-2 FIS or varIn contains type-2 membership functions, parameters sets the UpperParameters property of the added membership function.

varIn — Fuzzy variable

fisvar object

Fuzzy variable, specified as a fisvar object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: fis = addMF(fis,"distance",Name="high")

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: fis = addMF(fis,"distance","Name","high")

Name — Membership function name

string | character vector

Membership function name, specified as a string or character vector. The default membership function name is "mf<uniqueIndex>", where uniqueIndex is automatically generated based on the current number of membership functions in the associated variable.

VariableType — Variable type

"input" | "output"

Variable type, specified as one of the following:

• "input" — Input variable

• "output" — Output variable

If your system has an input variable with the same name as an output variable, specify which variable to add the membership function to VariableType.

This name-value pair does not apply when adding when adding a membership function to a fisvar object.

LowerScale — Lower membership function scaling factor

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

Lower membership function scaling factor for type-2 membership functions, 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.

This name-value pair applies only when adding type-2 membership functions.

LowerLag — Lower membership function delay factor

[0.2 0.2] (default) | scalar value between 0 and 1 | vector of length 2

Lower membership function delay factor for type-2 membership functions, specified as a scalar value or a vector of length two. You can specify lag values between 0 and 1, inclusive.

This name-value pair applies only when adding type-2 membership functions.

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.

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.

Output Arguments

fisOut — Fuzzy inference system

mamfis object | sugfis object | mamfistype2 object | sugfistype2 object

Fuzzy inference system, specified as one of the following:

• mamfis object — Mamdani fuzzy inference system

• sugfis object — Sugeno fuzzy inference system

• mamfistype2 object — Type-2 Mamdani fuzzy inference system

• sugfistype2 object — Type-2 Sugeno fuzzy inference system

fisOut contains the added membership function, with all other properties matching the properties of fisInfisOut contains the added membership function, with all other properties matching the properties of fisIn

varOut — Fuzzy variable

fisvar object

Fuzzy variable, returned as a fisvar object. varOut contains the added membership function, with all other properties matching the properties of varIn.

Version History

Introduced in R2018b

R2019b: Support for fuzzy inference system structures will be removed

Support for representing fuzzy inference systems as structures will be removed in a future release. Use mamfis and sugfis objects with this function instead. To convert existing fuzzy inference system structures to objects, use the convertfis function.

This change was announced in R2018b. Using fuzzy inference system structures with this function issues a warning starting in R2019b.

R2018b: Function renamed and method for specifying variable and membership function changed

The name and behavior of the addmf function has changed. Now:

• addmf is addMF

• You specify the variable to which you want to add the membership function by name rather than by index.

• You specify the name of the membership function using a name-value pair argument.

These changes require updates to your code.

Update Code

The following table shows some typical usages of addmf for adding membership functions to fuzzy variables and how to update your code. In this table, fis is a fuzzy inference system with two inputs, service and food, and one output, tip.

If your code has this form:	Use this code instead:
fis = addmf(fis'input',1,... 'poor',... 'gaussmf',[1.5 0])	fis = addMF(fis,"service",... "gaussmf",[1.5 0], 'Name',"poor")
fis = addmf(fis,'input',2,... 'rancid',... 'trapmf',[-2 0 1 3])	fis = addMF(fis,"food",... "trapmf",[-2 0 1 3],... 'Name',"rancid")
fis = addmf(fis,'output',1,... 'cheap',... 'trimf',[0 5 10])	fis = addMF(fis,"tip",... "trimf",[0 5 10],... 'Name',"cheap")