Fuzzy Sets

Verb: fuzzySet

Available from: <Enterprise>

Defines a fuzzy set based on its membership function.

Syntax

fuzzySet --function(FuzzyMembershipFunctions) --sets(String) --shape(Nullable<FuzzyShapes>) --edge(FuzzyEdges) --m1(Numeric) --m2(Numeric) --m3(Numeric) --m4(Numeric) --minimum(Numeric) --maximum(Numeric) (FuzzySet)=value

Inputs

Script Designer Required AcceptedTypes Description
--function Function Required FuzzyMembershipFunctions Function that defines the degree of membership of a given element to the set, returning actual values between 0 and 1. Options:
  • Piecewise Linear
  • Trapezoidal
    		•
    --sets Sets Only whenFunction is PiecewiseLinear Text Text with Piecewise Linear coordinates to form the function.
    Format: (x1, y1); (x2, y2); ...; (xn, yx), where x refers to the x coordinate of the Cartesian plane and y refers to the y coordinate of the Cartesian plane
    --shape Shape Only whenFunction is Trapezoidal FuzzyShapes Trapezoidal function shape used to specify the coordinates of the fuzzy set membership function. Options:
  • Flat
  • Flat With Range
  • Number
  • Number With Range
  • Triangular
  • Triangular With Range
    		•
    --edge Edge Only whenShape is Reserved_Edge FuzzyEdges Defines the edge format that is used in Trapezoidal. Options:
  • Left
  • None
  • Right
    		•
    --m1 M1 Only whenShape is Reserved_M1 Number Number that defines the value of the "x" coordinate of the first point of Trapezoidal.
    M1 values:
  • For Number, Triangular or Flat: 0;
  • For Number With Range, Triangular With Range or Flat With Range: This is the value defined in Minimum.
    • --m2 M2 Only whenShape is Reserved_M2 Number Number that defines the value of the "x" coordinate of the second point of Trapezoidal.
    M2 values:
  • For Number, Triangular or Flat: 1;
  • For Number With Range, Triangular With Range or Flat With Range: This is the value defined in Maximum.
    • --m3 M3 Only whenShape is Reserved_M3 Number Number that defines the value of the "x" coordinate for the third point of Trapezoidal.
    M3 values:
  • For Triangular: 0;
  • For Triangular With Range: The value defined in Minimum;
  • For Flat: 1;
  • For Flat With Range: This is the value defined in Maximum.
    • --m4 M4 Only whenShape is Reserved_M4 Number Number that defines the value of the "x" coordinate for the fourth point of Trapezoidal.
    M4 values:
  • For Flat: 0;
  • For Flat With Range: This is the value defined in Minimum.
    • --minimum Minimum Only whenShape is Reserved_Min Number Defines the minimum return value of the specified fuzzy set membership function.
    --maximum Maximum Only whenShape is Reserved_Max Number Defines the maximum return value of the specified fuzzy set membership function.

    Outputs

    Script Designer AcceptedTypes Description
    value Result Fuzzy Set Returns a variable of the "Fuzzy Set" type, which contains the fuzzy set specified in the input parameters.

    Example

    First, a fuzzy logic set is started with Begin Fuzzy with Intervals = 1000. Next, fuzzy logic is created to tell the quality of service of a restaurant. Then, the End Fuzzy command is used to terminate the set.

    defVar --name low --type FuzzySet
defVar --name medium --type FuzzySet
defVar --name good --type FuzzySet
defVar --name serviceQuality --type Fuzzy
defVar --name foodQuality --type Fuzzy
defVar --name littleTip --type FuzzySet
defVar --name reasonableTip --type FuzzySet
defVar --name generousTip --type FuzzySet
defVar --name tip --type Fuzzy
defVar --name foodGrade --type Numeric --value "7.5"
defVar --name serviceGrade --type Numeric --value 6
defVar --name tipValue --type Numeric
beginFuzzy --intervals 1000
   fuzzySet --function "Trapezoidal" --shape "Number" --edge "Right" --m1 0 --m2 5 low=value
   fuzzySet --function "Trapezoidal" --shape "Triangular" --m1 3 --m2 5 --m3 7 medium=value
   fuzzySet --function "Trapezoidal" --shape "Number" --edge "Left" --m1 5 --m2 10 good=value
   fuzzyVariable --left 0 --right 10 --labels "${low} ${medium} ${good}" serviceQuality=value
   fuzzyVariable --left 0 --right 10 --labels "${low} ${medium} ${good}" foodQuality=value
   fuzzySet --function "Trapezoidal" --shape "Number" --edge "Right" --m1 0 --m2 12.5 littleTip=value
   fuzzySet --function "Trapezoidal" --shape "Triangular" --m1 6.25 --m2 12.5 --m3 18.75 reasonableTip=value
   fuzzySet --function "Trapezoidal" --shape "Number" --edge "Left" --m1 12.5 --m2 25 generousTip=value
   fuzzyVariable --left 0 --right 25 --labels "${littleTip} ${reasonableTip} ${generousTip}" tip=value
   
//The food was rancid or the service was poor.
   fuzzyRule --name "Terrible food or service" --condition "${foodQuality} IS ${low} OR ${serviceQuality} IS ${low}" --variable ${tip} --set ${littleTip}
   
//The service was reasonable.
   fuzzyRule --name "Average service" --condition "${serviceQuality} IS ${medium}" --variable ${tip} --set ${reasonableTip}
   
//The food was delicious or the service was good.
   fuzzyRule --name "Great Food or Service" --condition "${foodQuality} IS ${good} OR ${serviceQuality} IS ${good}" --variable ${tip} --set ${generousTip}
endFuzzy
setVar --name "${foodQuality}" --value "${foodGrade}"
setVar --name "${serviceQuality}" --value "${serviceGrade}"
evaluate --expression "${tip}" tipValue=value
logMessage --message "Tip Value: ${tipValue};\r\nFood Grade: ${foodGrade};\r\nService Grade: ${serviceGrade}" --type "Info"

    See Also

  • Begin Fuzzy
  • End Fuzzy
  • Fuzzy Rule
  • Fuzzy Variable