membership function

introduce:

definition:

If there is a number A(x)∈[0, 1] corresponding to any element x in the domain of discourse (the scope of research) U, then A is called a fuzzy set on U, and A(x) It is called the membership degree of x to A. When x changes in U, A(x) is a function called the membership function of A.

Parameter Description:

The closer the degree of membership A(x) is to 1, the higher the degree of x belonging to A, and the closer A(x) is to 0, the lower the degree of x belonging to A. The degree to which x belongs to A is represented by the membership function A(x) whose value is in the interval (0, 1).

Related knowledge description

The degree of membership belongs to the concept in the fuzzy evaluation function: fuzzy comprehensive evaluation is a very effective multi-factor decision-making method for making a comprehensive evaluation of things affected by multiple factors. Its characteristic is that the evaluation result is not absolutely positive or negative. Instead, it is expressed as a fuzzy set.

Determination of membership function:

There is no mature and effective method for the establishment of membership function, and most of the establishment methods of the system are still based on experience and experiments. For the same fuzzy concept, different people will establish not exactly the same membership function, although the form is not exactly the same, as long as it can reflect the same fuzzy concept, it still leads to the same goal in solving and processing the actual fuzzy information. Several commonly used methods are described below.

Sigmoid membership function (dsigmf)

x=0:0.1:10;

y=smf(x,[1 8]);%1代表S的起点 8是终点

plot(x,y);

xlabel('函数输入值‘）；

ylabel('函数输出值’）；

grid on

insert image description here

Gaussian membership function (gaussmf)

x=0:0.1:10;
y=gaussmf(x,[2 5]); %5是中心 2是宽度
plot(x,y);
xlabel('函数输入值')
ylabel('函数输出值')
grid on

insert image description here

Generalized Bell Membership Function (gbellmf)

x=0:0.1:10;

y=gbellmf(x,[2 4 6]);%2是底 4是腰 6是最高峰

plot(x,y);


xlabel('函数输入值')
ylabel('函数输出值')

grid on

insert image description here

Trapezoidal membership function (trapmf)

x=0:0.1:10;

y=trapmf(x,[1 5 7 8]);%1代表S的起点 8是终点 峰值是5和7

plot(x,y);

xlabel('函数输入值‘）；

ylabel('函数输出值’）；

grid on

insert image description here

Triangular membership function (trimf)

x=0:0.1:10;

y=trimf(x,[2 6 7]);

plot(x,y);

xlabel('函数输入值‘）；

ylabel('函数输出值’）；

grid on

insert image description here

Z-shaped membership function (zmf)

x=0:0.1:10;

y=zmf(x,[2 6]); %2是起点 6是终点

plot(x,y);

xlabel('函数输入值‘）；

ylabel('函数输出值’）；

grid on

insert image description here

ps：没有公式的讲解，但是隶属度函数的公式也十分简单，如果感兴趣的话，可以在网上查阅学习