What is fuzzy theory, foundation and process

1、 What is fuzzy theory

Fuzzy theory ： Use the degree of belonging instead of strictly belonging to or not belonging to （ If someone is tall 0.8）

The fuzzy logic ： A convenient way to map input space to output space , It is a powerful tool to deal with imprecision and nonlinearity quickly and effectively .

such as ： Weekly changes

The classic collection is divided into two categories on Friday and Saturday , It's mutated

Fuzzy sets are gradual on Friday and Saturday , Belong to [0,1] Membership function of

2、 Fuzzy sets

Membership function ： An element maps to [0,1] Section

Then fuzzy sets ：

among ,uA(x) Express x The collection A Membership of . The closer the 1, indicate x Belong to A The greater the degree of .

3、 Membership function ( Gradient curves ) Selection of

The membership function is an arbitrary curve that conforms to the problem description , It can be defined artificially

Determine the method ： Comparative ranking method of the second academy 、 Fuzzy statistics ( statistical )、 Fitting fuzzy distribution method 、 Minimum ambiguity method 、 Expert experience method

（ Generally, the existing applicable membership function can be directly selected ）

 4、 Fuzzy operation

Standard Boolean logic operation

2 The operation of a classical set

 

 

Writing method of fuzzy logic operation

2 The operation of a fuzzy set

Fuzzy sets correspond to membership functions one by one , Therefore, the fuzzy operation of fuzzy sets is equivalent to the fuzzy operation between membership functions

 rij Is the membership function calculated according to the specific problem  

 

 

5、 Fuzzy comprehensive evaluation

  

The weight of each factor can be determined subjectively , Or determined by objective weighting method  

Fuzzy evaluation matrix r Evaluate every factor u Belong to each evaluation V The degree of  .

4 One factor ,3 Comments , Then the evaluation matrix is 4x3 Matrix , as follows

 

 A Is the weight of each factor .

  

 6、 Case study

If there is no factor weight , Calculate with weighting algorithm  

  Next, calculate the membership function of each factor

 

 

 

Interval data , It is suitable to use trapezoidal membership function

Value data , It is suitable to use triangle membership function

You can first make a schematic diagram of the segmented function of the data , Then find the appropriate membership function , Then complete the formula of piecewise function