sugfistype2

Interval type-2 Sugeno fuzzy inference system

Description

Use a sugfistype2 object to represent an interval type-2 Sugeno fuzzy inference system (FIS).

As an alternative to a type-2 Sugeno system, you can create a:

• Type-2 Mamdani system using a mamfistype2 object

• Type-1 Sugeno system using a sugfis object

• Type-1 Mamdani system using a mamfis 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 type-2 Sugeno FIS object, use one of the following methods:

• The sugfistype2 function.

• If you have input/output data, you can use the genfis function. You can then convert this FIS to a type-2 system using convertToType2.

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

• Convert an existing type-2 Mamdani FIS to a Sugeno FIS using convertToSugeno.

Syntax

fis = sugfistype2

fis = sugfistype2(Name,Value)

Description

fis = sugfistype2 creates a type-2 Sugeno FIS with default property values. To modify the properties of the fuzzy system, use dot notation.

fis = sugfistype2(Name,Value) specifies FIS configuration information or sets object properties using name-value pair arguments. You can specify multiple name-value pairs. Enclose names in quotes.

Input Arguments

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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 the comma-separated pair consisting of 'NumInputs' and 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 the comma-separated pair consisting of 'NumInputMFs' and a positive integer.

NumOutputs — Number of FIS outputs

0 (default) | nonnegative integer

Number of FIS outputs, specified as the comma-separated pair consisting of 'NumOutputs' and 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 the comma-separated pair consisting of 'NumOutputMFs' and a positive integer.

MFType — Membership function type

"trimf" (default) | "gaussmf"

Membership function type for input variables, specified as the comma-separated pair consisting of 'MFType' and 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 — Flag for automatically adding rules

"allcombinations" (default) | "none"

Flag for automatically adding rules, specified as the comma-separated pair consisting of "AddRules" and 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.

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)

Defuzzification method for computing crisp output values from the aggregated output fuzzy set. Type-2 Sugeno systems support only weighted-average defuzzification.

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) = [];

DisableStructuralChecks — Flag for disabling consistency checks

false (default) | true

Flag for disabling consistency checks when property values change, specified as a logical value.

By default, when you change the value of a property of a sugfistype2 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 DisableSturcturalChecks to true.

Note

Disabling structural checks can result in an invalid sugfistype2 object.

To reenable the consistency checks, first verify that the changes you made to the FIS are consistent and produce a valid sugfistype2 object. Then, set DisableSturcturalChecks to false. If the sugfistype2 object is invalid, reenabling the consistency checks generates an error.

TypeReductionMethod — Type-reduction method

"karnikmendel" (default) | "ekm" | "iasc" | "eiasc" | string | function handle

Type-reduction method for converting a type-2 output fuzzy set to an interval type-1 fuzzy set, specified as one of the following:

• "karnikmendel" — Karnik-Mendel

• "ekm" — Enhanced Karnik-Mendel

• "iasc" — Iterative algorithm with stop condition

• "eiasc" — Enhanced iterative algorithm

• String — Name of a custom type-reduction function in the current working directory or on the MATLAB path.

• Function handle — Function handle to a custom type-reduction function in the current working folder or on the MATLAB path.

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

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
convertToType1	Convert type-2 fuzzy inference system into type-1 fuzzy inference system

Examples

Create Type-2 Sugeno Fuzzy Inference System

Create a type-2 Sugeno fuzzy inference system with default property values.

fis = sugfistype2;

Modify the system properties using dot notation. For example, set the type reduction method to use the enhanced Karnik-Mendel method.

fis.TypeReductionMethod = "ekm";

Alternatively, you can specify one of more FIS properties when you create a fuzzy system.

fis = sugfistype2('TypeReductionMethod',"ekm");

Specify Number of Inputs and Outputs for Type-2 Sugeno System

Create a type-2 Sugeno fuzzy inference system with three inputs and one output. A type-2 Sugeno system uses type-2 membership functions only for its input variables.

fis = sugfistype2("NumInputs",3,"NumOutputs",1)

fis = 
  sugfistype2 with properties:

                       Name: "fis"
                  AndMethod: "prod"
                   OrMethod: "probor"
          ImplicationMethod: "prod"
          AggregationMethod: "sum"
      DefuzzificationMethod: "wtaver"
                     Inputs: [1x3 fisvar]
                    Outputs: [1x1 fisvar]
                      Rules: [1x27 fisrule]
    DisableStructuralChecks: 0
        TypeReductionMethod: "karnikmendel"

	See 'getTunableSettings' method for parameter optimization.

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