How to calculate the fuzzy comprehensive evaluation index? How to calculate the four fuzzy operators?

One 、 application

  Fuzzy comprehensive evaluation is based on some concepts of fuzzy mathematics , Provide evaluation for actual comprehensive evaluation problems , That is, fuzzy comprehensive evaluation is based on fuzzy mathematics , Applying the principle of fuzzy relation composition , Some boundaries are unclear 、 Quantifying factors that are not easy to quantify , And then a method of comprehensive evaluation .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘ Fuzzy comprehensive evaluation ’ Button . Here's the picture

（2） Drag and drop the data and click start analysis

PS： If there are evaluation index weights , Don't forget to drag and drop data

3、 ... and 、SPSSAU Analysis steps

Four 、 Case study

background

A clothing brand produces a new style of clothing , To understand the consumer's acceptance of this style . There are five evaluation indicators （ They are the designs and colors , Style , Price , Durability , Comfort ）, There are four comments （ They are very welcome , welcome , commonly , Do not welcome ）. Now I hope to analyze the comprehensive evaluation of consumers , In the end is very welcome , Or welcome , Or they are not welcome . The weights of the five indicators are （0.1,0.1,0.15,0.3,0.35）. This case selects the weighted average type .

5、 ... and 、 analysis

Put data into analysis box ,SPSSAU The system automatically generates analysis results , as follows ：

Calculation formula

1. Membership

(1) The weight distribution vector of each factor is set as A : A =(0.1,0.1,0.15,0.3,0.35)( The first column of the case data )

(2) The index evaluation vector is set as R：R1=(0.2,0.5,0.3,0.0);R2=(0.1,0.3,0.5,0.1);R3=（0.0,0.1,0.6,0.3）;R4= （0.0,0.4,0.5,0.1）;R5=(0.5,0.3,0.2,0.0)

  among ,R1、R2、R3、R4、R5 Combined into a fuzzy evaluation matrix R.

  Make fuzzy transformation （B）:B=AR;

 2. Membership normalization

example ：

And so on .

6、 ... and 、 summary

  It can be seen from the above table that , in the light of 5 Indicators , as well as 4 Fuzzy comprehensive evaluation of comment sets , And use M(., +) Operator ;
Firstly, the weight vector matrix of evaluation index is established A, And build 5x4 Weight judgment matrix R, Finally, it is analyzed that 4 Weight values of comment sets , Namely ：0.205,0.320,0.390,0.085.
  It can be seen from the above table that ,4 The general weight value in the comment sets is the highest (0.390), According to the law of maximum membership , The final comprehensive evaluation result is " commonly ".

7、 ... and 、 Expand

1.SPSSAU Provide comprehensive score calculation

2.M（Λ,V）

example ：

First look at the left side of the equal sign , The first number on the left 0.1 And the first number in the first column on the right 0.1 Compare , Take the smaller as the result , Namely 0.1; And then the second number on the left 0.2 And the second number in the first column on the right 0.3 Compare , Take the small , by 0.2; The third number on the left 0.3 And the third number in the first column on the right 0.2 Compare , Take small as 0.2; Take the end of the process , Then take the big one , These three results are compared , Take the big one as the final result , The first column is 0.2, And so on .

For short, take the small first and then the large ;

3.M（ ,V）

example ：

  The first number of the matrix on the left 0.2 The first number in the first column on the right 0.1 ride , The second number on the left 0.3 And the second number in the first column on the right 0.3, The third number on the left 0.3 The third number in the first column on the right 0.1 ride , Then take the big of the three results .

For short, multiply first and then take the largest ;

4. M(Λ,+)

example ：

  First look at the left side of the equal sign , The first number on the left 0.1 And the first number in the first column on the right 0.1 Compare , Take the smaller as the result , Namely 0.1; And then the second number on the left 0.2 And the second number in the first column on the right 0.3 Compare , Take the small , by 0.2; The third number on the left 0.3 And the third number in the first column on the right 0.1 Compare , Take small as 0.1; The first three results are 0.1,0.2,0.1, Sum these three to get the first number to the right of the equal sign 0.4, And so on .（PS： Pay attention to the sum , If the result of summing is more than 1 Big , So the result is to take 1.）

abbreviation Take the small and then sum ;