The membership function
(MF) designs a structure of practical relationship to relational structure numerically where the elements lies between 0 and 1.
It also performs the process of desfusification by the centroid method which determines the output of the fuzzy system finding the center of the area under the curve of the membership function
that is relevant.
The trapezoidal membership function
was considered for the very low and very high variables.
1st layer, fuzzification layer: Each node in this layer is adaptive and outputs of the nodes consist of a membership degree depending on the membership function
used and values of independent variables.
Each trait is described using the membership function
, and a value of zero or one is assigned to it, as expressed in a fuzzy set.
The division created by membership function
is sufficient to set up a full-fledged light transmission coefficient and thickness fuzzy logic model.
The Interval Type 2 fuzzy set has a fuzzy membership function
, the membership grade for each element of this set is a fuzzy set in [0,1], as can be observed in [31-35].
To diligently adjust the membership function
of the fuzzy inference system (FIS), the ANFIS employs the least squares method and back-propagation gradient descent method from neural network .
A fuzzy subset A of a universe of discourse U is characterized by a membership function
[[mu].sub.A]: U [right arrow] [0, 1] which associates with each element x of U a number [[mu].sub.A](x) in the interval [0, 1] which represents the grade of membership of x in A.
Development of embedded fuzzy applications : a fuzzy logic control of washing machines uses a triangular membership function
for the control of washing machines based on specification of the degree of dirt on clothes and it also specifies the amount of soap needed to wash the clothes .
Here, [x.sub.i] [member of] U, [[mu].sub.A]: U [right arrow] [0, 1] is the membership function
of A, and [[mu].sub.A](x) [member of] [0, 1] is the degree of membership of x in A .
The paper was focused on two planner integer models and a solution method for solving the problem using the concept of tolerance membership function
and a set of Pareto optimal solutions.