sugfis

Sugeno fuzzy inference system

Description

Use a sugfis object to represent a type-1 Sugeno fuzzy inference system (FIS).

As an alternative to a type-1 Sugeno system, you can create a:

• Type-1 Mamdani system using a mamfis object

• Type-2 Sugeno system using a sugfistype2 object

• Type-2 Mamdani system using a mamfistype2 object

For more information on the different types of fuzzy inference systems, see Mamdani and Sugeno Fuzzy Inference Systems and Type-2 Fuzzy Inference Systems.

Creation

To create a Sugeno FIS object, use one of the following methods:

• The sugfis function.

• If you have input/output data, you can use the genfis function.

• If you have a FIS file (*.fis) for a Sugeno system, you can use the readfis function.

• Convert an existing Mamdani FIS to a Sugeno FIS using convertToSugeno.

Syntax

fis = sugfis

fis = sugfis(Name=Value)

Description

fis = sugfis returns a Sugeno FIS with default property values. To modify the properties of the fuzzy system, use dot notation.

fis = sugfis(Name=Value) specifies FIS configuration information or sets object properties using one or more name-value arguments.

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: NumInputs=2 configures the fuzzy system to have two input variables

NumInputs — Number of FIS inputs

0 (default) | nonnegative integer

Number of FIS inputs, specified as a nonnegative integer.

NumInputMFs — Number of membership functions for each FIS input

3 (default) | positive integer

Number of membership functions for each FIS input, specified as a positive integer.

NumOutputs — Number of FIS outputs

0 (default) | nonnegative integer

Number of FIS outputs, specified as a nonnegative integer.

NumOutputMFs — Number of membership functions for each FIS output

3 (default) | positive integer

Number of membership functions for each FIS output, specified as a positive integer.

MFType — Membership function type

"trimf" (default) | "gaussmf"

Membership function type for input variables, specified as either "trimf" (triangular MF) or "gaussmf" (Gaussian MF). For each input variable, the membership functions are uniformly distributed over the variable range with approximately 80% overlap in the MF supports.

Output membership functions are set to "constant" and uniformly distributed over the output variable ranges.

AddRules — Option for automatically adding rules

"allcombinations" (default) | "none"

Option for automatically adding rules, specified as one of the following:

• "allcombinations" — If both NumInputs and NumOutputs are greater than zero, create rules with antecedents that contain all input membership function combinations. Each rule consequent contains all the output variables and uses the first membership function of each output.

• "none" — Create a FIS without any rules.

Name — FIS name

"fis" (default) | string | character vector

FIS name, specified as a string or character vector.

This argument sets the Name property.

AndMethod — AND operator method

"prod" (default) | "min" | string | character vector | function handle

AND operator method for combining fuzzified input values in a fuzzy rule antecedent, specified as one of the following:

• "prod" — Product of fuzzified input values

• "min" — Minimum of fuzzified input values

• String or character vector — Name of a custom AND function in the current working folder or on the MATLAB^® path

• Function handle — Custom AND function in the current working folder or on the MATLAB path

This argument sets the AndMethod property.

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on fuzzy operators and the fuzzy inference process, see Fuzzy Inference Process.

OrMethod — OR operator method

"probor" (default) | "max" | string | character vector | function handle

OR operator method for combining fuzzified input values in a fuzzy rule antecedent, specified as one of the following:

• "probor" — Probabilistic OR of fuzzified input values. For more information, see probor.

• "max" — Maximum of fuzzified input values.

• String or character vector — Name of a custom OR function in the current working folder or on the MATLAB path.

• Function handle — Custom OR function in the current working folder or on the MATLAB path.

This argument sets the OrMethod property.

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on fuzzy operators and the fuzzy inference process, see Fuzzy Inference Process.

ImplicationMethod — Implication method

"prod" (default)

Implication method for computing consequent fuzzy set, specified as "prod". Sugeno systems always use the "prod" implication method, which scales the consequent membership function by the antecedent result value.

This argument sets the ImplicationMethod property.

For more information on implication and the fuzzy inference process, see Fuzzy Inference Process.

AggregationMethod — Aggregation method

"sum" (default)

Aggregation method for combining rule consequents, specified as "sum". Sugeno systems always use the "sum" aggregation method, which is the sum of the consequent fuzzy sets.

This argument sets the AggregationMethod property.

For more information on aggregation and the fuzzy inference process, see Fuzzy Inference Process.

DefuzzificationMethod — Defuzzification method

"wtaver" (default) | "wtsum"

Defuzzification method for computing crisp output values from the aggregated output fuzzy set, specified as one of the following:

• "wtaver" — Weighted average of all rule outputs

• "wtsum" — Weighted sum of all rule outputs

This argument sets the DefuzzificationMethod property.

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on defuzzification and the fuzzy inference process, see Fuzzy Inference Process.

DisableStructuralChecks — Option to disable consistency checks

false (default) | true

Option to disable consistency checks when property values change, specified as a logical value.

By default, when you change the value of a property of a sugfis object, the software verifies whether the new property value is consistent with the other object properties. These checks can affect performance, particularly when creating and updating fuzzy systems within loops.

To disable these checks, which results in faster FIS construction, set DisableStructuralChecks to true.

Note

Disabling structural checks can result in an invalid sugfis object.

To reenable the consistency checks, first verify that the changes you made to the FIS are consistent and produce a valid sugfis object. Then, set DisableStructuralChecks to false. If the sugfis object is invalid, reenabling the consistency checks generates an error.

This argument sets the DisableStructuralChecks property.

Properties

Name — FIS name

"fis" (default) | string | character vector

FIS name, specified as a string or character vector.

AndMethod — AND operator method

"prod" (default) | "min" | string | character vector | function handle

AND operator method for combining fuzzified input values in a fuzzy rule antecedent, specified as one of the following:

• "prod" — Product of fuzzified input values

• "min" — Minimum of fuzzified input values

• String or character vector — Name of a custom AND function in the current working folder or on the MATLAB path

• Function handle — Custom AND function in the current working folder or on the MATLAB path

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on fuzzy operators and the fuzzy inference process, see Fuzzy Inference Process.

OrMethod — OR operator method

"probor" (default) | "max" | string | character vector | function handle

OR operator method for combining fuzzified input values in a fuzzy rule antecedent, specified as one of the following:

• "probor" — Probabilistic OR of fuzzified input values. For more information, see probor.

• "max" — Maximum of fuzzified input values.

• String or character vector — Name of a custom OR function in the current working folder or on the MATLAB path.

• Function handle — Custom OR function in the current working folder or on the MATLAB path.

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on fuzzy operators and the fuzzy inference process, see Fuzzy Inference Process.

ImplicationMethod — Implication method

"prod" (default)

Implication method for computing consequent fuzzy set, specified as "prod". Sugeno systems always use the "prod" implication method, which scales the consequent membership function by the antecedent result value.

For more information on implication and the fuzzy inference process, see Fuzzy Inference Process.

AggregationMethod — Aggregation method

"sum" (default)

Aggregation method for combining rule consequents, specified as "sum". Sugeno systems always use the "sum" aggregation method, which is the sum of the consequent fuzzy sets.

For more information on aggregation and the fuzzy inference process, see Fuzzy Inference Process.

DefuzzificationMethod — Defuzzification method

"wtaver" (default) | "wtsum"

Defuzzification method for computing crisp output values from the aggregated output fuzzy set, specified as one of the following:

• "wtaver" — Weighted average of all rule outputs

• "wtsum" — Weighted sum of all rule outputs

For more information on using custom functions, see Build Fuzzy Systems Using Custom Functions.

For more information on defuzzification and the fuzzy inference process, see Fuzzy Inference Process.

DisableStructuralChecks — Option to disable consistency checks

false (default) | true

Option to disable consistency checks when property values change, specified as a logical value.

By default, when you change the value of a property of a sugfis object, the software verifies whether the new property value is consistent with the other object properties. These checks can affect performance, particularly when creating and updating fuzzy systems within loops.

To disable these checks, which results in faster FIS construction, set DisableStructuralChecks to true.

Note

Disabling structural checks can result in an invalid sugfis object.

To reenable the consistency checks, first verify that the changes you made to the FIS are consistent and produce a valid sugfis object. Then, set DisableStructuralChecks to false. If the sugfis object is invalid, reenabling the consistency checks generates an error.

Inputs — FIS input variables

vector of fisvar objects

FIS input variables, specified as a vector of fisvar objects. To add and remove input variables, use addInput and removeInput, respectively. You can modify the properties of the input variables using dot notation.

You can also create a vector of fisvar objects and assign it to Inputs using dot notation.

You can add membership functions to input variables using the addMF function.

Outputs — FIS output variables

vector of fisvar objects

FIS output variables, specified as a vector of fisvar objects. To add and remove output variables, use addOutput and removeOutput, respectively.

You can also create a vector of fisvar objects and assign it to Outputs using dot notation.

You can add membership functions to output variables using the addMF function.

Rules — FIS rules

vector of fisrule objects

FIS input variables, specified as a vector of fisrule objects. To add fuzzy rules, use the addRule function.

You can also create a vector of fisrule objects and assign it to Rules using dot notation.

To remove a rule, set the corresponding rule vector element to []. For example, to remove the tenth rule from the rule list, type:

fis.Rules(10) = [];

Sugeno systems do not support rules with NOT logic in the consequent.

Object Functions

addInput	Add input variable to fuzzy inference system
removeInput	Remove input variable from fuzzy inference system
addOutput	Add output variable to fuzzy inference system
removeOutput	Remove output variable from fuzzy inference system
addRule	Add rule to fuzzy inference system
addMF	Add membership function to fuzzy variable
removeMF	Remove membership function from fuzzy variable
evalfis	Evaluate fuzzy inference system
writeFIS	Save fuzzy inference system to file
convertToType2	Convert type-1 fuzzy inference system into type-2 fuzzy inference system

Examples

Create Sugeno Fuzzy Inference System

Create a Sugeno fuzzy inference system with default property values.

fis = sugfis;

Modify the system properties using dot notation. For example, configure fis to use weighted-sum defuzzification.

fis.DefuzzificationMethod = "wtsum";

Alternatively, you can specify one of more FIS properties when you create a fuzzy system. For example, create a Sugeno fuzzy system with specified AND and OR methods.

fis = sugfis(AndMethod="min",OrMethod="max");

Specify Number of Inputs and Outputs for Sugeno System

Create a Sugeno fuzzy inference system with three inputs and one output.

fis = sugfis(NumInputs=3,NumOutputs=1)

fis = 
  sugfis with properties:

                       Name: "fis"
                  AndMethod: "prod"
                   OrMethod: "probor"
          ImplicationMethod: "prod"
          AggregationMethod: "sum"
      DefuzzificationMethod: "wtaver"
    DisableStructuralChecks: 0
                     Inputs: [1×3 fisvar]
                    Outputs: [1×1 fisvar]
                      Rules: [1×27 fisrule]

	See 'getTunableSettings' method for parameter optimization.

By default, the software creates a rule for each possible input combination.

Create Sugeno FIS with Linear Output Membership Functions

Load a Sugeno FIS from a file.

fis = readfis("sugeno1");

The output variable has two membership functions. View the properties of the first membership function.

fis.Outputs(1).MembershipFunctions(1)

ans = 
  fismf with properties:

          Type: "linear"
    Parameters: [-1 -1]
          Name: "line1"

View the properties of the second membership function.

fis.Outputs(1).MembershipFunctions(2)

ans = 
  fismf with properties:

          Type: "linear"
    Parameters: [1 -1]
          Name: "line2"

The input membership functions and rules define which of these output functions are expressed and when.

fis.Rules

ans = 
  1×2 fisrule array with properties:

    Description
    Antecedent
    Consequent
    Weight
    Connection

  Details:
                    Description           
         _________________________________

    1    "input==low => output=line1 (1)" 
    2    "input==high => output=line2 (1)"

Plot the input membership functions of this system. The low membership function generally refers to input values less than zero, while high refers to values greater than zero.

plotmf(fis,"input",1)

Plot the output surface for this FIS.

gensurf(fis)

The overall fuzzy system output switches smoothly from the line called line1 to the line called line2.

Alternative Functionality

App

You can interactively create a Sugeno FIS using the Fuzzy Logic Designer or Neuro-Fuzzy Designer apps. You can then export the system to the MATLAB workspace.

Version History

Introduced in R2018b

R2018b: Replaces newfis

This function replaces newfis for creating Sugeno fuzzy inference systems.