Types of Membership functions

Types of Membership functions
1- Triangular Membership Function
Triangular function is defined by the following equation:


Triangular (x;a,b,c) =




Where a and b and c represent the x_coordinate for capital triangle, x represents the real value (Crisp Value) from the private variable fuzzy universe of discourse.
Function outputs ranging between 0 and 1 and represents the value of the degree of membership of x. b has a value of 1 membership degree, increase membership degree of elements located between a and b closer to the element of b, while the elements located between b and c are considerably less degree its membership slowly closer to the element of c. Figure 1 shows an example of the triangular function when the operators:
a= 3 و b = 5 و c= 8
2- Trapezoidal Membership Function:
This function is described using the following equation:
Trapezoidal (x;a,b,c,d) =
Where :
x: represents real value (Crisp Value) within the universe of discourse.
a, b, c, d represent a x- coordinates of the four heads of the trapezoidal and values should validated the following condition:
a < b < c < d