defuzziffy-methods function

Function to defuzzify fuzzy data

Function to defuzzify fuzzy data

This function defuzzifies FuzzyData into single value. The FuzzyData can only contain one fuzzy number, otherwise the defuzzification is not possible.

defuzziffy(fuzzyData, type = "mean")

## S4 method for signature 'FuzzyData'
defuzziffy(fuzzyData, type = "mean")

Arguments

  • fuzzyData: A FuzzyData
  • type: A "character" representing type of defuzzification. Currently implemented methods are "Yager", "modalValue", "modalValueDominancy", "mean". The default value is "mean".

Returns

A numeric value of defuzzified value, based on deffuzification method.

Details

The triangular fuzzy numbers AA represented as triplet [a1,a2,a3][a1,a2,a3] are defuzzified using these methods: "Yager":

def(A~)=(a2−a1)(a1+2/3(a2−a1)+(a3−a2)(a2+1/3(a3−a2))(a2−a1)+(a3−a2))def(A)=((a2−a1)(a1+2/3(a2−a1)+(a3−a2)(a2+1/3(a3−a2)))/((a2−a1)+(a3−a2))) def (\tilde{A}) = \frac{(a2-a1)(a1+2/3(a2-a1)+(a3-a2)(a2+1/3(a3-a2))}{(a2-a1)+(a3-a2))}def(A) = ((a2-a1)(a1+2/3(a2-a1)+(a3-a2)(a2+1/3(a3-a2))) / ((a2-a1)+(a3-a2)))

"modalvalue":

def(A~)=a2def(A)=a2 def (\tilde{A}) = a2def(A) = a2

"modalValueDominancy":

def(A~)=(a1+4∗a2+a3)/6def(A)=(a1+4∗a2+a3)/6 def(\tilde{A}) = (a1 + 4*a2 + a3)/6def(A) = (a1 + 4*a2 + a3)/6

"mean":

def(A~)=(a1+a2+a3)/3def(A)=(a1+a2+a3)/3 def(\tilde{A}) = (a1 + a2 + a3)/3def(A) = (a1 + a2 + a3)/3

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