Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 9, No. 3, 2023 

 

162 

Analysis	of	the	Advantages	and	Disadvantages	of	Four	
Comprehensive	Evaluation	Methods	
Mingyang Liu, Wenge Qin Shuang Yang 

Business School (School of Quality Management and Standardization), Foshan University, Jiangwan Street, Chancheng District, Foshan 
528000, China 

 

Abstract: This paper introduces the AHP, entropy value method, TOPSIS method and fuzzy comprehensive evaluation method 
in the comprehensive evaluation method, and analyzes the advantages and disadvantages of the four from the perspectives of 
subjectivity and objectivity, acceptance of decision makers, and difficulty of evaluation. The value method depends on the 
amount of initial data, the AHP research results are too subjective, the TOPSIS research conclusions do not fit the reality, and 
the results of the fuzzy comprehensive evaluation may have poor resolution. Finally, suggestions are put forward for the 
application scope of the four methods of single use and combined use. It is believed that the four evaluation methods can be 
combined in pairs or three, such as: entropy weight-TOPSIS, AHP-TOPSIS or entropy weight-AHP -Methods such as fuzzy 
comprehensive evaluation method avoid being affected by the limitations of a single evaluation method. 

Keywords: AHP, TOPSIS method, Entropy value method, Fuzzy comprehensive evaluation method. 
 

1. Introduction 
Comprehensive evaluation refers to the process of 

conducting a general analysis of the evaluation object 
according to different evaluation purposes, using the 
information of the evaluated object, selecting systematic, 
standardized and scientific evaluation methods [1]. However, 
since different evaluation methods calculate, process or 
analyze the object to be evaluated differently, the final results 
obtained using different evaluation methods may be different, 
which is possible As a result, the results of the evaluation did 
not meet the actual needs. Therefore, it is necessary to analyze 
the advantages and disadvantages of the four evaluation 
methods based on the analysis of AHP, TOPSIS method, 
entropy value method, and fuzzy comprehensive evaluation 
principle, and then consider the joint use according to their 
respective advantages and disadvantages Avoid being 
affected by shortcomings in evaluation methods. 

2. Introduction to the Method 

2.1. Entropy method 
2.1.1. Rationale 

The entropy value method is a representative objective 
empowerment method in comprehensive evaluation, which 
calculates the weight of indicators according to the amount of 
data information and the degree of mutual difference of the 
evaluated objects.  The concept of entropy was proposed by 
the German physicist Clausius as a measure of the degree of 
disorder of the system, and the entropy weight refers to the 
weight of an evaluated index [2]. The entropy method 
calculates the weight of the index according to the size of the 
observations of the sample data and the degree of difference 
between them, if the difference between the sample 
observations of the index of an evaluated object is smaller, 
proving that the indicator provides less information, the 
greater the entropy of the indicator. At the same time, it means 
that the less information the indicator provides to decision-
makers, the smaller the entropy weight; When the sample 
observations of the index are completely consistent, the 

entropy value reaches the maximum, indicating that the index 
basically does not provide useful information to decision 
makers, and the entropy weight reaches the minimum value. 
Conversely, if the difference between the indicator 
observations is large, proving that the indicator observations 
provide useful information, the smaller the entropy value, the 
greater the entropy weight.  

2.1.2. Basic usage steps 
(1) Establish a matrix to be evaluated for m objects to be 

evaluated and n evaluation indicators, substitute the original 
data, and obtain the matrix 

𝑅 （𝑋）  
Among them, 𝑥 it is the original data of the ith evaluation 

object on the jth evaluation index.  
(2) Data standardization, due to the different dimensional 

dimensions, positive and negative directions of different 
original data under different evaluation indicators, in order to 
make the data under different evaluation indicators can be 
compared with each other, so the initial data should be 
dimensionless. The methods of dimensionless processing of 
data include squared sum normalization, intervalization, 
forwardization, negative orientation, and 𝑀𝑖𝑛
𝑚𝑎𝑥normalization [3]. In the entropy method, normalization 
is generally chosen because it is necessary to make the 
processed raw data present a linear relationship with the 
original data.𝑀𝑖𝑛 𝑚𝑎𝑥 The processed data is𝑦 .  

(3) Normalization under each evaluation object𝑦 . Let the 
normalized data be normalized 𝛾 as follows 

𝛾 𝑦 / 𝑦  

(4) Calculate the entropy value of the evaluation index of 
item j, 𝐻 where,𝑘 1/𝑙𝑛 𝑚 

𝐻 𝑘 𝛾 ln 𝛾  

(5) Calculate the difference coefficient and 𝐺  entropy 
weight of the jth index𝑊  



 

163 

𝐺 1 𝐻 𝑊 𝐺 / 𝐺  

(6) Through the entropy weight, the evaluation results of m 
objects to be evaluated under n evaluation indicators are 
calculated𝑠 .  

𝑠 𝑊 𝛾  

2.2. AHP 
2.2.1. Rationale 

The analytic hierarchy method (AHP) is a representative 
subjective empowerment method in comprehensive 
evaluation. AHP in the complex decision-making problems of 
multi-objective, multi-evaluation indicators and multi-
program, through the subjective experience judgment of 
decision-makers, will The overall judgment of multiple 
evaluation indicators in the whole question becomes a "two-
by-two comparison" of each evaluation index, and then 
determines the relative importance of each evaluation index 
at each level [4]. Finally, the subjective empirical judgment 

of the decision maker is synthesized, and each evaluation 
index at each level is weighted.  

2.2.2. Basic usage steps 
(1) Clarify the problem and establish a hierarchical 

hierarchy according to the mutual subordination of many 
indicators. Divide the problem to be decided into three layers: 
the target layer, the criteria layer, and the indicator layer. 
There is only one element in the target layer, which is the final 
goal to be decided. The criterion layer and the indicator layer 
can have multiple elements.  

(2) Construct a comparative judgment matrix B, use the 
subjective experience judgment of decision makers, and 
subjectively evaluate and score the elements in the criterion 
layer and the index layer according to the importance 
comparison between elements. In AHP, the importance scale 
between indicators is expressed using 1-9 and its reciprocal 
[5]. Assuming that the ratio of the importance of criterion A to 
criterion B in the criterion layer is 2, the ratio of criterion B 
to criterion A is 1/2 of importance. The specific scales 
between 1-9 are meaningfully defined in the following table.  

 
Table 1. Indicator Meaning 

Factor i is better than factor J Quantified value 

Equally important 1 

Slightly more important 3 

Strong is important 5 

Strongly important 7 

Extremely important 9 

The middle value of two adjacent judgments 2, 4, 6, 8 

reciprocal aij=1/aji 

 
The final constructed judgment matrix B form is as follows: 

𝐵

𝑏  𝑏 ⋯ 𝑏
𝑏  𝑏

⋮
… 𝑏

⋮
𝑏  𝑏 ⋯ 𝑏

𝑏 0，𝑏 1，𝑏 1/𝑏  

(𝑏 is the ratio of the importance of factor I to factor J). 
(3) Hierarchical single ranking, through mathematical 

calculation of the weight of each index of a certain level 
compared to a certain index of the previous level. The 
calculation of hierarchical single sorting can be obtained by 
judging the eigenroots and eigenvectors of the matrix: 

𝐵 𝑊 𝜆 𝑊 
where 𝜆 is the 𝐵largest feature root, is the 

𝑊normalized feature vector, and the component 𝜆 is the 
𝑊𝑤 weight value of the hierarchical single ranking of the 
corresponding element.  

(4) Consistency test, in order to avoid logical errors such 
as "element A is more important than element B, element B 
is more important than element C, and element C is more 
important than element A", it is necessary to perform a 
consistency test on the judgment matrix B. The consistency 
test is done by defining and calculating the consistency 
metric𝐶 , random consistency metric, 𝑅 and consistency 
ratio CR.  

𝐶 𝐶𝑅 Among them, the value of is 

determined according to the dimension of the judgment 
𝑅 matrix, and it is generally believed that if the value of CR 
is less than or equal to 0.1, the consistency test of the 
judgment matrix is passed, otherwise it is necessary to check 
whether the judgment matrix has a logical error.  The 
values of the matrix of order 1-9 𝑅 can be referred to the 
table below.  

 
Table 2. 𝑅  values 

n 1 2 3 4 5 6 7 8 9 
𝑅  0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 

 
(5) Overall ranking of levels, sorting the elements of the 

criterion layer and indicator layer layer by layer from top to 
bottom, and finally obtaining the final weight of each 
indicator. After the end of the hierarchical total sorting, it is 
also necessary to perform a consistency test [6] on the 
hierarchical total sorting, and the test formula is as follows: 

𝐶𝑅
∑ 𝑏 𝐶
∑ 𝑏 𝑅

 

where 𝑏 is the weight of the benchmark layer. 𝐶 It is a 
consistency test indicator and a 𝑅 random consistency 
indicator.  



 

164 

2.3. TOPSIS law 
2.3.1. Rationale 

TOPSIS (Technique for Order Preference by Similarity to 
an Ideal Solution) method is a commonly used comprehensive 
evaluation method, which constructs the "positive ideal 
solution" and "negative ideal solution" of the scheme to be 
evaluated by making full use of the original data information. 
Then each evaluation object is sorted by calculating the 
Euclidean distance between the "positive ideal solution" and 
the "negative ideal solution" of each evaluation object. 
Among them, the optimal evaluation object is the closest to 
the "positive ideal solution" and the farthest from the 
"negative ideal solution". Conversely, the worst evaluation 
object is the closest to the "negative ideal solution" and the 
farthest from the "positive ideal solution". Among them, the 
"positive ideal solution" is the most ideal scheme for each 
evaluation object, because there is probably no "positive ideal 
solution" and "negative ideal solution" in reality, so TOPSIS 
is also called "the ordering method that is infinitely close to 
the ideal solution" [7].  

2.3.2. Basic usage steps 
(1) Construct a data matrix, assuming that there are m 

objects to be evaluated, in order to analyze each different 
evaluation object, which covers a total of n evaluation 
indicators, wherein The resulting raw data matrix is as follows: 

𝑋

𝑟
𝑟

𝑟
𝑟 ⋯

𝑟
𝑟

⋮ ⋱ ⋮
𝑟 𝑟 ⋯ 𝑟

 𝑟 is the original value of the ith 

evaluation object under the jth indicator.  
(2) Because the original data dimensions are different, the 

positive and negative indicators in the original data need to 
eliminate the dimensions, and the methods of dimensionless 
processing of the data include squared sum normalization, 
intervalization, positiveization, negative orientation and 
normalization, etc., and the original data after processing is 
set to𝑚𝑖𝑛 𝑚𝑎𝑥𝑥.  

(3) Determine the "positive ideal solution" and "negative 
ideal solution", the formula is as follows: 

Positive ideal solution: 𝐻
𝑚𝑎𝑥 𝑥 ，𝑥 ， ⋯ 𝑥 |𝑗 ∈

𝑆 ， 𝑚𝑖𝑛 𝑥 ，𝑥 ， ⋯ 𝑥 |𝑗 ∈ 𝑆  
Negative ideal solution: 𝐻

𝑚𝑖𝑛 𝑥 ，𝑥 ， ⋯ 𝑥 |𝑗 ∈
𝑆 ， 𝑚𝑎𝑥 𝑥 ，𝑥 ， ⋯ 𝑥 |𝑗 ∈ 𝑆  

Among 𝑆  them𝑆 , it is a benefit-type index and a cost-
oriented index [8].  

(4) Calculate the distance between each object to be 
evaluated and the distance between the positive ideal solution 
and the distance between the negative ideal 
solution𝑠𝑒𝑝 :𝑠𝑒𝑝  

𝑠𝑒𝑝 ∑ 𝑥 𝐻 𝑠𝑒𝑝 ∑ 𝑥 𝐻      

(j=1,2，...，n) 
(5) Calculate the comprehensive evaluation index of each 

object to be evaluated𝐶 , and the formula is as follows: 

𝐶
𝑠𝑒𝑝

𝑠𝑒𝑝 𝑠𝑒𝑝
 

(6) Sort 𝐶 each object to be evaluated according to the size 
of the value, and the larger the comprehensive evaluation 
index of the object to be evaluated, the better the object to be 
evaluated.  

2.4. Vague comprehensive evaluation 
2.4.1. Rationale 

Fuzzy comprehensive evaluation uses fuzzy mathematics 
and uses the principle of fuzzy relationship synthesis to 
quantify the fuzzy concept, so as to comprehensively evaluate 
the advantages and disadvantages of the objects to be 
evaluated. This method is mainly used to understand the 
ambiguity of the problem to be solved, and to convert 
qualitative evaluation into quantitative evaluation according 
to the membership theory of fuzzy mathematics [9].  

2.4.2. Basic usage steps 
(1) Determine the set of indicators of the object to be 

evaluated𝑋 𝑥 ，𝑥 ， ⋯ 𝑥 , which is the M index of the 
object to be evaluated. where x is the element in the 
evaluation indicator.  

(2) Establish a collection of comments on evaluation 
indicators𝑉. Set 𝑉 𝑣 ，𝑣 ， ⋯ 𝑣 this to be the N rating 
of comments of the object to be evaluated. The review set is 
a necessary factor for fuzzy evaluation, and the review level 
will be used to vaguely evaluate the indicators of the 
evaluation object.  

(3) Establish a fuzzy relationship matrix𝑅.  

𝑅

𝑟 𝑟
𝑟 𝑟 ⋯

𝑟
𝑟

⋮ ⋱ ⋮
𝑟 𝑟 ⋯ 𝑟

 

where m represents the number of evaluation indicators and 
n represents the number of evaluation levels. 𝑟 Indicates the 
degree to which an indicator of the object being evaluated is 
affiliated to 𝑥  a fuzzy subset of the 𝑉 comment set𝑣  . Here 
requires normalization of the degree of membership, 
i.e.∑ 𝑟 1  

The 𝑥 evaluation of an object to be evaluated in terms of 
an indicator is described 𝑟 𝑟 ，𝑟 ， ⋯ 𝑟  , in other 
words, the degree vector of the degree of affiliation of an 
index to the set of comments of an object to be evaluated 𝑥 is 
𝑉 where n indicates n 𝑟 𝑟 ，𝑟 ， ⋯ 𝑟   kinds of 
comments or grades. All membership vectors form the fuzzy 
relation matrix R.  

(4) Determine the weight of the index, in order to reflect 
the importance of each index to be evaluated, set the index 
weight for each index to be evaluated 𝑊
𝑤 ，𝑤 ， ⋯ 𝑤  . An element in this weight vector 𝑤  is 

essentially the degree of membership of the metric 𝑥 to the 
entire set of metrics𝑋. Requested here𝑤 0， ∑ 𝑤 1.  

(5) Establish fuzzy comprehensive evaluation, select 
appropriate fuzzy operators, and generally select all-factor 
weighted average fuzzy synthetic operators [10]. Obtain the 
result vector𝑊 𝑅 𝑏 ，𝑏 ， ⋯ 𝑏 𝐵. where vector B 
needs to be normalized.∑ 𝑏 1   Indicates 𝑏   the degree 
of affiliation of the evaluated object as a whole𝑣 .  

(6) The final results of fuzzy comprehensive evaluation are 
analyzed. The final result vector is the degree of affiliation of 
the evaluated object to 𝑉 each level in the review set. This 
result is analyzed using the maximum membership principle 
and the weighted average principle.  



 

165 

3. The Analysis of Advantages and 
Disadvantages 

3.1. Entropy method 
3.1.1. Advantages 

The entropy method only calculates the weight of the index 
from the amount of data information and the degree of mutual 
difference of the object to be evaluated, and does not mix the 
subjective judgment of the decision maker in the evaluation 
process, and can not be affected by human factors, so the 
objectivity of the evaluation results is strong. At the same time, 
the entropy method has no requirements for the number of 
evaluation indicators and the amount of data in the evaluation 
index, so the entropy method has a wide range of applications, 
and the obtained weights can be combined with other 
comprehensive evaluation methods. Finally, the calculation 
process of the entropy method is more convenient, and the 
weight of each evaluation index obtained is easy for decision-
makers to understand.  

3.1.2. Disadvantages 
First of all, the evaluation process of the entropy method is 

easily affected by the dimensionality of the original data, 
because the dimensions of different data are different, so the 
original data needs to be dimensionless before using the 
entropy method to evaluate. The dimensionless processing 
method will affect the value of the new data generated, which 
will affect the final evaluation result.  

Secondly, the entropy method cannot reflect the decision-
maker's understanding of the importance of each index, 
because the entropy method is calculated only by data, which 
is easily affected by the difference in data observations, and 
there will be a situation where the weight of an important 
index is small instead of the weight of the importance index 
is large. For example, if the difference in the observed values 
of the data under an important indicator is too small, the 
entropy value will be too large and the final entropy weight 
will be too small, which is contrary to the understanding of 
decision makers [11].  

Third, the role of the entropy method is limited to 
determining the weight of the index to be evaluated, so it may 
not help the decision-maker to make the final decision, and it 
will be of limited help to the decision-maker in practical 
application.  

Finally, the use of the entropy method depends on the initial 
amount of data, but if the initial amount of data is small, the 
use of the entropy method may result in the calculated entropy 
weight being inaccurate and may contradict the facts.  

3.2. AHP 
3.2.1. Advantages 

AHP establishes a hierarchical hierarchical structure based 
on many objects to be evaluated, which will obtain a clear 
combination of weights for decision makers, which can avoid 
the cognitive bias of traditional subjective determination due 
to too many indicators to be evaluated. In addition, AHP 
transforms the vague importance comparison between 
various indicators into a clear quantitative comparison, so that 
the importance of different indicators at the same level has a 
clear quantitative identification, which is not affected by the 
original data [12]. Finally, the weights obtained by AHP are the 
subjective judgments of different decision-makers, and the 
evaluation results are more in line with the subjective 
intentions of decision-makers, while the final results are 

objectively calculated, so that the final evaluation results of 
AHP take into account subjectivity and objectivity, and the 
conclusions drawn have strong adaptability and can be 
combined with different comprehensive evaluation methods.  

3.2.2. Disadvantages 
The disadvantages of AHP are obvious, first of all, the 

objects to be evaluated should not be too much, otherwise the 
hierarchical structure established will be more complicated, 
the overly complex evaluation matrix will also make the 
amount of calculation too large, and the consistency test of 
the evaluation matrix will lead to the whole process of AHP 
being slightly complicated. Second, when comparing 
indicators in pairs, decision-makers' judgments will be 
influenced by their own subjective wishes and preferences, 
and may not reflect actual needs, and if there are slightly more 
indicators in one level, it will also make it difficult for 
decision-makers to subjectively judge and score, even if they 
use 1-9 Scaling tends to lead decision-makers to make 
contradictory judgments. Finally, the results obtained by AHP 
are not fixed, and with the same hierarchical structure, 
decision-makers may make different evaluation matrices in 
different situations to obtain different evaluation results [13].  

3.3. TOPSIS law 
3.3.1. Advantages 

First of all, the TOPSIS method does not have too many 
restrictions on the number of objects to be evaluated and the 
number of indicators in the original data, and the applicability 
is strong, regardless of the objects to be evaluated and the 
number of indicators, the TOPSIS method can always find the 
"positive ideal solution" and "negative ideal solution" of the 
object to be evaluated And calculate the relative closeness. At 
the same time, the TOPSIS method is not affected by the 
subjective empirical judgment of decision-makers, and the 
closeness of the "positive and negative ideal solution" 
calculated in the evaluation process only relies on the original 
data, and the evaluation results are relatively objective. 
Secondly, the evaluation results directly obtained by the 
TOPSIS method can rank the advantages and disadvantages 
of the evaluation objects, which is convenient for decision-
makers to make decisions. Finally, the TOPSIS method makes 
full use of the original data, so that the final evaluation results 
are both holistic and local [14].  

3.3.2. Disadvantages 
Since the TOPSIS method calculates the closeness of the 

object to be evaluated and the "positive and negative ideal 
solution", the setting of the "positive ideal solution" is only to 
combine the best positive indicators, and the setting of the 
"negative ideal solution" is only to combine the worst 
negative indicators, and all positive indicators are combined  
The "positive ideal solution" may conflict between indicators, 
and the evaluation results may not be close to reality, as well 
as the "negative ideal solution". In other words, considering 
the closeness of the object to be evaluated to the "positive 
ideal solution" and "negative ideal solution" may be contrary 
to reality when the evaluation indicators may conflict with 
each other. Therefore, when using the TOPSIS method, it is 
necessary to consider the actual situation of the object to be 
evaluated and the evaluation index to avoid the situation that 
the "ideal solution" is not in line with the reality, which will 
increase the workload during the evaluation.  

Secondly, the ranking obtained by the TOPSIS method is 
only the ranking of relative fit, and the size of the relative fit 
is not similar to the intuitive "weight" obtained by AHP or 



 

166 

entropy methods, and the relative fit as a numerical value may 
not enable decision-makers to distinguish grades for each 
object to be evaluated [15].  

Finally, the TOPSIS method has a high dependence on the 
weight of each index to be evaluated, and the weight between 
the indicators in the TOPSIS method will affect the final 
evaluation result, while the weight setting of the index may 
be subjective, and different index weight settings may affect 
the objectivity of the final evaluation.  

3.4. Vague comprehensive evaluation 
3.4.1. Advantages 

Firstly, the evaluation results of fuzzy comprehensive 
evaluation are relatively clear, and the fuzzy comprehensive 
evaluation obtains the fuzzy evaluation vector through the 
calculation of the weight vector and the fuzzy relationship 
matrix, and then analyzes it through the principle of 
maximum membership degree or weighted average principle, 
which can intuitively observe what grade or interval the final 
evaluation result is in, which is convenient for decision-
makers to make decisions. It also facilitates comparison 
between different subjects to be evaluated.  

Secondly, because the set of comments and indicators of 
fuzzy comprehensive evaluation are realistic, and the fuzzy 
relationship matrix is determined by the scores of many 
evaluators, the results of fuzzy comprehensive evaluation 
have strong "accuracy", "systematicness" and "credibility" 。  

Finally, fuzzy comprehensive evaluation can quantify the 
original qualitative problems, deal with the ambiguous 
evaluation objects through accurate numerical means, and 
make a more scientific, reasonable and realistic quantitative 
evaluation of the data containing ambiguity in information, so 
that the fuzzy comprehensive evaluation has a wider scope of 
application [16].  

3.4.2. Disadvantages 
It can be seen from the use process of fuzzy comprehensive 

evaluation that fuzzy comprehensive evaluation is a more 
subjective evaluation method, which is mainly manifested in 
the setting of weight vectors may be subjective settings of 
decision makers, and the data of the fuzzy relationship matrix 
is also based on the subjective judgment of the evaluator, and 
the choice of fuzzy operators may not be determined by 
objective facts, so the final evaluation result of fuzzy 
comprehensive evaluation has a high degree of subjectivity 
and may contradict the facts.  

Second, similar to AHP, at different times, different judges 
are likely to give different evaluation results, so that the final 
judgment results cannot be highly fixed.  

Finally, when the number of index sets is large, because the 
weight vector of the index needs to be normalized, the weight 
coefficient of the relative membership degree may be small, 
and the resolution of the results obtained by fuzzy 
comprehensive evaluation is poor, resulting in the failure of 
the evaluation.  Finally, fuzzy comprehensive evaluation is 
similar to TOPSIS, and the indicators in the index set of fuzzy 
comprehensive evaluation also need to be empowered, so the 
different weights of indicators will also affect the evaluation 
results of fuzzy comprehensive evaluation.  

4. Scope of Application and 
Suggestions for Use 

4.1. Scope of application 
The entropy method and AHP are both used to give weights 

to the indicators to be evaluated, unlike the entropy method, 
which gives weights based on the initial data, while AHP 
relies on the evaser's empirical judgment. Therefore, when the 
object to be evaluated has rich initial data, it is recommended 
to use the entropy method, while the object to be evaluated 
does not have initial data or has less initial data, and AHP can 
be used. The same is true for TOPSIS method and fuzzy 
comprehensive evaluation, when the object to be evaluated 
has rich initial data, the TOPSIS method can be used to 
determine the relative proximity to the "positive ideal 
solution" and "negative ideal solution" to judge the order of 
the object to be evaluated, and if there is no rich initial data, 
the index set and comment set can be established, and the 
fuzzy comprehensive evaluation can be used by the scoring 
method.  

The four comprehensive evaluation methods can be applied 
to evaluate the competitiveness of industries and products, but 
if a comprehensive evaluation method is used alone, it will be 
affected by the disadvantages of this method, so when it is 
necessary to evaluate an object to be evaluated, two or three 
of the four methods can be used.  

4.2. Recommendations for use 
4.2.1. Entropy weight-TOPSIS, AHP-TOPSIS 

When using the TOPSIS method for evaluation, if the 
weight of the evaluation index is not set, the TOPSIS method 
defaults to the equal weight of each index, which is often not 
in line with reality, so it is necessary to manually assign 
weight to the evaluation index, at this time, if the initial data 
is richer, you can choose the entropy method to determine the 
weight of the evaluation index to obtain the entropy weight, 
and then assign the entropy weight to the index to be 
evaluated, and then use the TOPSIS method to calculate the 
relative closeness. The entropy weight obtained by combining 
the entropy method with the TOPSIS method - the TOPSIS 
method can take into account the objective weight of the 
entropy method and the objective ranking of the TOPSIS 
method, and at the same time, Since both the entropy method 
and the TOPSIS method do not limit the number of evaluation 
objects and the number of indicators too high, the use of 
entropy weight-TOPSIS to evaluate the objects to be 
evaluated will not be caused by excessive data  Impact 
evaluation process and results.  

When the initial amount of data is small, the entropy value 
method to calculate the entropy weight will not be accurate 
enough, so the AHP method can be used to weight each index 
to be evaluated, and then the weight can be assigned to the 
index to be evaluated, and the final result can be obtained by 
using the TOPSIS method.  

4.2.2. AHP-fuzzy comprehensive evaluation, entropy 
weight-fuzzy comprehensive evaluation 

When the initial data of the indicators of the fuzzy 
comprehensive evaluation is small, and the subjective will of 
the decision makers is strong, the AHP can choose to 
empower the indicators, and then use the AHP-fuzzy 
comprehensive evaluation method to obtain the final 
evaluation results. When the initial data of the index of fuzzy 
comprehensive evaluation is large and objective weight is 
required, the entropy weight-fuzzy comprehensive evaluation 
method can be used to weight the index.  

These two methods can form a more systematic 
"empowerment-evaluation" system, with a wide range of 
applications and scientific methods.  



 

167 

4.2.3. Entropy weight-AHP-fuzzy comprehensive 
evaluation 

The entropy method is more objective and avoids the 
subjective experience judgment of decision-makers, but it is 
difficult to reflect the importance that decision-makers attach 
to evaluation indicators. AHP empowerment can extract the 
subjective intentions of decision-makers, but it is easy to 
contradict objectivity. Therefore, the evaluation method of 
combining entropy and AHP can be used to determine the 
entropy weight-AHP combined with AHP by the entropy 
value method. When using entropy weight-AHP, there are 
three approaches.  

(1) The entropy method is used for indicators with more 
objective weights, while AHP is used for indicators with more 
subjective weights.  

(2) The entropy method was used to obtain the objective 
weight, 𝑊 the AHP was used to obtain the subjective weight, 
and then the preference coefficient was used to obtain the 
subjective and objective comprehensive weighting to obtain 
the comprehensive weight 𝑊 𝛼𝑊 [17]. The formula is as 
follows: 

𝑊 𝛼𝑊 （1 𝛼）𝑊  
(3) Construct a hierarchical model, use the entropy method 

to calculate the weights for the indicators that need objective 
evaluation, and then replace the 1-9 evaluation scale of the 
decision-makers in AHP according to certain conversion 
standards, and finally obtain the weights measured by AHP, 
which can effectively avoid the strong subjectivity of 
decision-makers in AHP.  

For the evaluation system combining subjectivity and 
objectivity, entropy weight-AHP empowerment can be used, 
and then combined with fuzzy comprehensive evaluation to 
obtain the entropy weight-AHP-fuzzy comprehensive 
evaluation method [18]. This avoids the evaluation method 
from losing one over the other in the evaluation process.  

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