Maxima methods for defuzzification: FoM, LoM and MoM
Maxima methods are quite simple but not as trivial as lambda cut methods. Maxima methods rely on the position of maximum membership of an element at a particular position in a fuzzy set.
The set of methods under maxima methods we will be discussing here are:
- Height method
- First of maxima (FoM)
- Last of maxima (LoM)
- Mean of maxima (MoM)
Height method:
This method is based on the Max-membership principle and is defined as follows.
ÎŧC(x*) âĨ ÎŧC(x), âx â X
Note: This method is applicable when height is unique.
Example:
First of Maxima (FoM) method:
Determine the smallest value of the domain with maximized membership degree
FoM = First of Maxima: xâ = minâĄ{ x | ÎŧC(x) = h(C) }
Last of Maxima (LoM) method:
Determine the largest value of the domain with maximized membership degree
LoM = Last of Maxima: xâ = max{ x | ÎŧC(x) = h(C) }
Example: First of Maxima and Last of Maxima
Find the defuzzification value for a given fuzzy set
First of Maxima: xâ = 1
Last of Maxima: xâ = 6
Watch on YouTube: Maxima Methods
Middle of Maxima (MoM) method:
In order to find the middle of maxima, we have to find the âmiddleâ of elements with maximum membership value
Where, M ={ xi |Â ÎŧC(xi) = h(C) }, Or M is the set of points having the highest membership value
Note: This method is applicable to symmetric functions only
Example: Middle of maxima
Find the deffuizified value for a given fuzzy set using the middle of the maxima method:
xâ = (a + b) / 2
xâ = (2 + 5) / 2
xâ = 3.5
Test Your Knowledge:
For the given fuzzy set Young, perform defuzzification using the following methods:
- First of Maxima (FoM)
- Last of Maxima (LoM)
- Middle of Maxima (MoM)
Please post your answer / query / feedback in comment section below !