Types of Membership functions

Types of Membership functions
1- Triangular Membership Function

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.

2- Trapezoidal Membership Function:

Real values which lies between b and c is the degree of membership 1, but values between a and b, the degree of membership increases closer to the element of b, while the elements located between c and d less than the degree of membership gradually closer to the element of d, and membership degree is zero otherwise. The diagram given below shows an example of the trapezoidal function when a = 1, b = 5, c = 7 and d = 8.


2.1 Leftmost Trapezoidal :
are trapezoidal function when value of c and d equal with the value of the last item in the universe of discourse, and sometimes a function is called Upward Slope. Elements between a and b increases its degree of membership whenever element is closer to b while elements between b and c has a membership degree 1.