Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 7, No. 2, 2023 

48 

Research	on	Information	Quality	Evaluation	Method	of	
Q&A	Community	from	the	Perspective	of	Fuzzy	
Evaluation	
-- Taking CSDN as an Example 

Dan Li* 

School of Management, Shanghai University, Shanghai, China 

Abstract: [Purpose/significance] Facing the current situation of information overload in the Q&A community, this paper 
discusses how to effectively evaluate the quality of information released in the community, so as to facilitate the staff of Q&A 
community to screen and recommend valuable and practical answers for platform users, which will enhance user stickiness. 
[Method/process] Firstly, the hesitant fuzzy information evaluation matrix is established for the qualitative evaluation 
information. Secondly, the entropy weight method is used to initially weight the indicators in consideration of the subjectivity of 
information matrix. Then, considering the overlap of indicator information, the initial weights are revised based on the correlation 
between the indicators to improve the accuracy of answer sorting. Finally, a comprehensive ranking of answer quality is obtained 
based on the weighted grey relational analysis method, and the optimal answer is selected. [Result/conclusion] An example of 
technical Q&A community from CSDN is selected to analyze. The results show that the hesitant fuzzy sets as evaluation 
information can effectively solve the problem of evaluation personnel’s judgment level difference, and the revised index 
weights are used to make the answer ranking more in line with the actual situation. 

Keywords: Q&A community, Information quality management, Hesitant fuzzy set, Grey relational analysis. 

1. Introduction
According to the 49th Statistical Report on the 

Development of the Internet in China, as of December 2021, 
the number of Internet users in China has reached 1.032 
billion, with 42.96 million new Internet users added in 
December 2020 [1]. More and more people rely on the 
Internet to find the information they need to deal with difficult 
problems and doubts they encounter in their studies, life or 
work. Social Q&A systems, or Q&A communities, are social 
platforms that focus on user knowledge sharing, whereby 
users post questions and exchange and interact with the 
community's answerers to share knowledge. As this think-
tank that brings together the wisdom of the masses is 
generated by users, unlike the answers of authoritative experts, 
the problem of uneven quality of information inevitably arises. 
Therefore, how to solve the problem of information quality in 
Q&A communities and realise effective interaction in Q&A 
communities has become a focus of attention for scholars at 
home and abroad. 

In the evaluation of online information resources, scholars 
have proposed different evaluation methods according to the 
characteristics of online information, for example, Wang 
Xianya et al. (2022) [2] used questionnaire survey method to 
study the quality of seller reputation information on e-
commerce platforms; Cheng Quan et al. (2020) [3] studied 
medical and health information based on the evaluation 
theory and method of evidence-based reasoning; Li Jun et al. 
(2021) [4] used fuzzy comprehensive evaluation method to 
evaluate provincial government information resource sharing 
platforms; Chen Yue and Deng Zhaohua (2019) [5] conducted 
a comprehensive evaluation of the influence of health care 
websites based on grey correlation analysis. As grey 
correlation analysis is more stable than the common 

comprehensive evaluation methods, some scholars later used 
it for information quality evaluation and continuously 
supplemented and optimized it. Scholars have chosen 
different assignment methods in the evaluation process. In 
order that the relative importance of indicators does not 
violate the common sense of decision makers, some scholars 
have used subjective assignment methods. Guo Shunli et al. 
(2017) [6] conducted an expert questionnaire to determine the 
indicator weights and assessed the credibility of C2C platform 
information based on a weighted grey correlation. Some 
scholars have also considered that subjective weighting is 
more arbitrary and less reliable for decision making, and 
adopted objective weighting method for indicators. Ma 
Zhonggui et al. (2006) [7] used grey correlation analysis to 
determine the weights of evaluation factors to study the 
problem of extracting useful information from Internet 
information. Cui Jie et al. (2008) [8] improved the subjective 
and objective integration method based on grey correlation to 
solve the weights of indicators, which made the importance 
of each indicator differ significantly. Yi Ming and Zhang 
Tingting (2019) [9] used rough sets to approximate and assign 
weights to indicators, and then solved the weighted grey 
correlation to quantify the similarity between alternative 
answers and ideal answers. This shows that grey correlation 
analysis can be used not only to determine the weight of 
indicators, but also for comprehensive evaluation. The use of 
grey correlation analysis for comprehensive evaluation better 
handles the information incompleteness in measuring the 
merits of solutions, and provides a powerful means of parsing 
out the ranking of solutions [10]. If the method is used to 
assign indicators to systems containing qualitative indicators, 
it is not easy to reduce the error and influence caused by 
subjective factors in the judging process. Therefore, this paper 
proposes to choose the grey correlation analysis method to 



 

49 

conduct a comprehensive assessment of alternative answers. 
For the characteristics of answer quality assessment in 

Q&A communities, the qualitative index values of answers 
need to be scientifically and rationally transformed into 
quantitative ones. Xu Yong et al. (2016) [11] proposed to 
establish a fuzzy comprehensive evaluation matrix to 
transform qualitative evaluation into quantitative evaluation, 
assigning weighted indicators based on the number of times 
the relevant indicator set was mentioned, and then conducting 
a comprehensive evaluation of Taobao product text reviews. 
The hesitant fuzzy information evaluation matrix provides an 
effective means to quantify qualitative indicator values, 
which can better reflect the judgmental disagreement existing 
among evaluators; however, ignoring the homogeneity among 
indicators in the assignment process may lead to inaccurate 
ranking results. Therefore, in this paper, we propose to use the 
hesitant fuzzy information evaluation matrix to quantify the 
qualitative indicators, adopt the entropy weighting method to 
objectively assign weights to the indicators, and then revise 
the initial weights based on the correlation measure among 
the indicators, based on which we use the weighted grey 
correlation analysis to rank the alternative answers. 

The rest of our paper is structured as follows: section 2 
reviews the related work; section 3 focuses on the model 
presented in this paper; section 4 presents the description and 
analysis of the experimental results and also the comparative 
experiments performed; section 5 discusses the advantages 
and limitations of the model summarizes and looks ahead. 

2. Traditional Grey Correlation 
Analysis 

Deng Julong (1987) [12] proposed a grey correlation 
analysis based on the geometric relationship between 
sequences to measure the strength of the relationship between 
things. After that, scholars at home and abroad have 
continuously improved the grey system doctrine and applied 
it to audit and evaluation, multi-attribute decision making and 
inference prediction. Its basic calculation process is as 
follows [12]. 

Let the set of scenarios be 𝑃 𝑃 , 𝑃 , ⋯ , 𝑃   and the 
data series reflecting the changing characteristics of each 
scenario be 𝑝 𝑘 , 𝑝 𝑘 , ⋯ , 𝑝 𝑘  , 𝑘 1,2, ⋯ , 𝑧 
respectively. The correlation coefficient of scenario 𝑃  to the 
reference scenario 𝑃  at moment 𝑘 is defined as 

 

𝜉 𝑝 𝑘 , 𝑝 𝑘
∆ ∆

| | ∆
         (1) 

 
where ∆ max max|𝑝 𝑘 𝑝 𝑘 | , ∆

min min|𝑝 𝑘 𝑝 𝑘 | , 𝑝 𝑘   are the ideal values at 

moment 𝑘, 𝜌 is the resolution factor, and 𝜌 ∈ 0,1 . 
The grey correlation between scenario 𝑃   and the 

reference scenario 𝑃  is 
 

𝑟 𝑃 , 𝑃 ∑ 𝜉 𝑝 𝑘 , 𝑝 𝑘              (2) 
 

Traditional grey correlation analysis can measure the 
closeness of the relationship between indicators and can also 
rank the solutions. Eq. (2) is the arithmetic mean of the grey 
correlation coefficients to obtain the grey correlation degree, 
which is slightly inadequate when dealing with decision 
problems containing multiple indicators with different 

weights. Therefore, the diversity between the qualitative 
assessment indicators of Q&A community answers will be 
addressed in this study, and differential weights will be 
assigned. 

3. Assessing the Quality of Quizzes 
Based on Grey Fuzzy Evaluation 
Method 

3.1. Establishing a Hesitant Fuzzy Information 
Evaluation Matrix 

Traditional information evaluation matrices are only 
suitable for quantitative indicators that are easy to use with 
deterministic numerical measures, and are flawed when 
measuring the quality of questions and answers that contain 
multiple qualitative indicators. Fuzzy evaluation matrices are 
particularly advantageous when faced with problems where 
the value of qualitative indicators is heavily influenced by 
subjective perceptions, as they can translate individual 
subjective thinking into data form. In addition, since 
evaluators have different modes of thinking and it is not easy 
to evaluate each indicator of an alternative answer with exact 
values, Hesitant Fuzzy Set (HFS) is chosen as evaluation 
information in this paper. 

Torra (2010) [13] proposed a set of possible values to 
quantitatively describe the hesitation problem encountered 
when making decisions, and the HFS was born. 

3.1.1. Hesitation Fuzzy Set 
Definition 1 [13]: let X be the given non-empty set that will 

𝐴 〈𝑥, ℎ 𝑥 〉|𝑥 ∈ 𝑋  
is called the Hesitant Fuzzy Set and is a mapping of 𝑋 →

0,1  , where ℎ 𝑥   is the Hesitant Fuzzy Element (HFE), 
denoting the possible affiliation of 𝑥 ∈ 𝑋 . The elements in 
ℎ 𝑥   are 𝛼  , 𝛼 ∈ 0,1  , 𝑘 1,2, ⋯ , 𝑙  , and 𝑙   denotes 
the number of elements contained in the HFE ℎ. 

In general, the elements of a given hesitant fuzzy element 
are arranged in an unordered manner. In order to facilitate the 
decision calculation, the elements of the hesitant fuzzy 
element ℎ 𝑥  shall be arranged in ascending order. 

In addition, the elements of a given hesitant fuzzy element 
are arranged in an unordered manner. To facilitate the 
decision calculation, the elements 𝛼  in the HFE ℎ 𝑥  shall 
be arranged in ascending order. 

3.1.2. Hesitation Fuzzy Element-Completion Strategy 
Typically, the HFEs in Hesitant Fuzzy Sets 𝐸 and 𝐹 are 

of unequal length, i.e. 𝑙 ℎ 𝑥 𝑙 ℎ 𝑥  , such that 
𝑙 max 𝑙 ℎ 𝑥 , 𝑙 ℎ 𝑥 . In order to enable the two 
HFSs to be characterized and compared, the set of fuzzy 
numbers with fewer fuzzy elements is filled so that it is the 
same length as the set with more fuzzy elements. The strategy 
of filling is influenced by the individual risk perception of the 
decision maker: risk averse people add the elemental 
minimum of the fuzzy element to the HFE with fewer 
elements, while risk preferences add the elemental maximum. 

In recent years the theory has been extended and applied to 
a variety of fields such as multi-attribute decision making, 
risk assessment, and semantic computing. 

3.2. Initial Configuration of Indicator Weights 
for HFSs Based on Fuzzy Cross-Entropy 

There are various methods for assigning indicators to 
multi-indicator evaluation problems, which can be subjective, 



 

50 

objective or combined to determine the indicator weights, but 
each method is applicable to different contexts. The HFS is to 
quantify the qualitative indicators, which is already subjective, 
so this paper mainly considers objective weighting. Liu Li et 
al. (2009) [14] determined the weight coefficients based on 
the entropy weight method, and assessed the water quality of 
the samples by an improved fuzzy comprehensive evaluation 
method. In the traditional fuzzy comprehensive evaluation 
method, most of the commonly used weight methods only 
consider the contribution made by a single indicator, without 
involving the connection between multiple things to be 
evaluated, and are unable to describe the impact of varying 
degrees of difference in the value of indicators on the weight 
distribution among indicators [14]. Since the entropy weight 
method can reflect the degree of effective information 
provided by each indicator in the problem, this paper will 
objectively assign weights to each indicator of the original 
evaluation value (i.e. Hesitant Fuzzy Set) of question and 
answer based on fuzzy cross-entropy, in order to preserve the 
large amount of information in the original indicators and 
avoid the loss of information caused by the conversion of 
indicators. The entropy measure is used to establish the initial 
weight of the indications based on the fuzzy properties of the 
original evaluation information. 

Theorem 1 [15]: Let ℎ  be a HFE, then the fuzzy cross-
entropy of ℎ is 

 
𝐸 ℎ 1 𝐶 ℎ, ℎ               (3) 

 
1

ln  

where 𝑇 1 𝑞 ln 1 𝑞 2 𝑞 ln 2 𝑞
ln 2  , 𝑞 0 . ℎ   is the kth smallest number in ℎ  and 
𝐶 ℎ, ℎ   denotes the self-cross entropy of ℎ . In general, 
indicators with small values of 𝐸 ℎ   should be assigned 
large weights; indicators with large values of 𝐸 ℎ  should be 
assigned small weights [15]. 

If there are 𝑚  alternative answers 𝑃 𝑖 1,2, ⋯ , 𝑚  , 𝑛 
indicators 𝐺 𝑗 1,2, ⋯ , 𝑛   with indicator weight vectors 
𝜔 𝜔 , 𝜔 , ⋯ , 𝜔  , 𝜔 ∈ 0,1  , 𝑗 1,2, ⋯ , 𝑛  and 
∑ 𝜔 1. Denote by ℎ  the set of possible degrees ℎ  
of alternative answer 𝑃   satisfying indicator 𝐺  , and use 
fuzzy cross-entropy to determine the indicator weights, as 
shown in Equation (4). 

 

𝜔
∑

, 𝑗 1,2, ⋯ , 𝑛             (4) 

 
where 𝐸 ∑ 𝐸 ℎ  . The fuzzy cross-entropy 

𝐸 ℎ  of the HFE ℎ  is calculated by Equation (3). 

3.3. Correction of Indicator Weights Based on 
Grey Correlation Analysis 

The previous step determines the indicator weights by 
fuzzy cross entropy, which effectively measures the 
importance of each indicator in the evaluation information 
with fuzzy characteristics. However, there may be 

overlapping associations between indicators in the 
assessment system, and the more similar the change trend of 
two indicator value series, the stronger the correlation 
between two indicators [16]. Fuzzy cross-entropy assignment 
does not take into account the overlapping information 
between indicators, resulting in less accurate assignment, 
while grey correlation analysis can measure the degree of 
correlation between indicators, so grey correlation analysis 
can be used to calculate the correlation coefficient between 
indicators and correct the initial weights to improve the 
accuracy of the weights. The specific steps are as follows. 

3.3.1. Integration of Elements in HFEs Based on 
Geometric Score Functions 

Definition 2: Let ℎ  be a HFE, then the geometric score 
function of ℎ  is 

 

𝑠 ℎ ∏ 𝛼              (5) 

 
where 𝛼  denotes the elements of the HFE ℎ . 
The geometric score of each HFE was calculated according 

to Equation (5), which in turn yielded the geometric score 
matrix 𝑆, as shown in Equation (6). 

 

𝑆
𝑠 ℎ … 𝑠 ℎ

⋮ ⋱ ⋮
𝑠 ℎ … 𝑠 ℎ

              (6) 

 

3.3.2. Measuring the Grey Correlation between Two 
Indicators 

Based on the geometric score matrix 𝑆, the grey correlation 
𝑟  between two indicators was calculated using Equations (1) 
and (2), which in turn led to the grey correlation matrix 𝐶  
between indicators, as shown in Equation (7). 

 

𝐶 𝑟
𝑟 … 𝑟

⋱ ⋮
𝑟

             (7) 

 
The greater the 𝑟 , the closer the two indicators' trends are, 

and the more comparable they are. 

3.3.3. Standardisation of 𝑪𝟏 Based on Minimum 
Correlation 

To increase the effective grey correlation, the grey 
correlation between the original indicators is normalised 
using the minimal correlation between indicators 𝛾
min

,
𝑟 . 

Definition 3: Let 𝐶 𝑟   be the grey correlation 
matrix between indicators in hesitant fuzzy multi-attribute 
decision making, then call 

 

𝐶 𝑑 𝛾 𝑟

𝛾
𝑟 …

𝛾
𝑟

⋱ ⋮
𝛾

𝑟

  (8) 

 
is the effective grey correlation matrix between indicators, 

where 
𝛾

𝑟   denotes the degree of independence between 

indicators. If 
𝛾

𝑟 1 , it means there is no correlation 

between two indicators; if 
𝛾

𝑟 1 , it means there is a 



 

51 

correlation between two indicators, and the smaller 
𝛾

𝑟 , the 

higher the correlation degree. 

3.3.4. Adjusting the Weights Obtained Based on Fuzzy 
Cross-Entropy 𝝎𝒋 

The weights of the indicators obtained from the entropy 
measure are corrected using the effective grey correlation 
matrix 𝐶 , as shown in Equation (9). 

 
𝜔 ′ 𝜔 ∏ 𝑑 ∏ 𝑑           (9) 

 
The adjusted indicator weights are 𝜔 ′

𝜔 ′, 𝜔 ′, ⋯ , 𝜔 ′ . Since ∑ 𝜔 ′ 1, they are readjusted 
as shown in Equation (10). 

 

𝜔 ′′
𝜔 ′

∑ 𝜔 ′               (10) 

 
So the final adjusted vector of indicator weights is 𝜔 ′′

𝜔 ′′, 𝜔 ′′, ⋯ , 𝜔 ′′ . 
Compared to the initial weight 𝜔 , the modified indicator 

weight 𝜔 ′′  eliminates the correlation information between 
two indicators and effectively improves the accuracy of 
assignment. 

3.4. Answer Quality Ranking Based on 
Improved Weighted Grey Correlation 
Expressed in HFSs 

Due to the ambiguity and uncertainty between the quality 
of Q&A community answers and their evaluation factors in 
this study, as well as the incomplete and unbalanced 
evaluation of information by evaluators with varied 
information reserves and information demands, the grey 
correlation analysis method is chosen to evaluate the 
similarity between the answers to be evaluated and the best 
answers in the Q&A community. The method quantifies 
factors with unclear boundaries and not easy to quantify, and 
overcomes the shortcomings of traditional multiple 
correlation analysis and multiple regression analysis [17]. The 
specific steps are as follows. 

3.4.1. Positive Processing of Decision Information 
Each indication has a different polarity; some are benefit 

indicators, while others are cost indicators. For the original 
hesitation fuzzy information matrix 𝐴 𝛼  , the 
expanded hesitation fuzzy information evaluation matrix 
𝐵 𝛽   is obtained after completing the HFEs. The 
standard unification of 𝐵 is performed by the normalization 
algorithm [18] to obtain the candidate answer evaluation 
square 𝐻 ℎ   with consistent vector directionality, 
i.e. the forward processing information set. 

When the indicator is of the benefit type, it is processed 
according to Equation (11). 

 

ℎ               (11) 

 
When the indicator is of the cost type, it is treated according 

to Equation (12). 
 

ℎ                (12) 

 
where ℎ  denotes the elements of the normalised HFE ℎ  

of the answer 𝑃  under the indicator 𝐺 . 

3.4.2. Identifying the Ideal Answer 𝑷𝝄 
The ideal solution 𝑃 ℎ , ℎ , ⋯ , ℎ   is derived for 

the hesitant fuzzy information evaluation matrix 𝐻
ℎ   following complementation and normalisation, 

where 𝑧 ∑ 𝑙
∙

 , ℎ max ℎ  , 𝑘 1,2, ⋯ , 𝑙
∙

 , 𝑡

1,2 ⋯ , 𝑧  and 𝑙
∙

  denotes the length of the HFE ℎ∙   under 
the indicator 𝐺 . 

3.4.3. Building a Sequence of Differences between the 
Ideal Answer 𝑷𝝄 and the Alternative Answer 𝑷𝒊 
Based on the HFSs of 𝑯 

Definition 4: Let 𝑃 ℎ , ℎ , ⋯ , ℎ   be the ideal 
answer, and 𝑃 ℎ , ℎ , ⋯ , ℎ  be the alternative answer, 
and ℎ 𝛼 , 𝛼 , ⋯ , 𝛼   be the inscription of a HFE 
containing 𝑙  possible affiliations. To subtract the HFE ℎ  
from ℎ . 

 
∆ ℎ ℎ 𝛼 𝛼 , 𝛼 𝛼 , ⋯ , 𝛼 𝛼  (13) 

 
where 𝑙   denotes the length of ℎ   (or ℎ  ). In this way 

∆ , ∆ , ⋯ , ∆   is computed and the final result of the 
subtraction operation of the two HFEs is obtained. 

3.4.4. Measuring the Grey Correlation between 
Alternative Answers and the Ideal Answer and 
Ranking the Answers 

First, the correlation coefficient of elements of HFEs in 
𝐻 ℎ   is calculated using Equation (1), where 𝑧 
denotes the total number of elements of all HFEs in the same 
answer sequence in 𝐻, i.e. 𝑧 ∑ 𝑙

∙
. 

Secondly, the correlation coefficient of all elements in each 
HFE in 𝐻 ℎ  is averaged to obtain the correlation 
coefficient of each HFE 𝜂 . 

 

𝜂 ∑ ,             (14) 

 
where λ 1 ∑ 𝑙  , 𝑖 1,2, ⋯ , 𝑚 , 𝑗

1,2, ⋯ , 𝑛. When 𝑗 1, λ 1. 
Next, the grey correlation coefficient matrix 𝑁 is formed 

from the correlation coefficients 𝜂  between each alternative 
answer and the ideal answer, as shown in Equation (15). 

 

𝑁 𝜂
𝜂 … 𝜂

⋮ ⋱ ⋮
𝜂 … 𝜂

          (15) 

 
Then the grey correlation 𝑅   between the alternative 

answer and the ideal answer is 
 

𝑅 ∑ 𝜂 𝜔 ′′  𝑖 1,2, ⋯ , 𝑚         (16) 
 
where 𝜔 ′′ represents the final indicator weights adjusted 

by Equations (9) and (10). 
Finally, the 𝑅  values are ranked, with the greater the grey 

correlation, the closer the answer is to the ideal answer. 



 

52 

4. Empirical Analysis 

4.1. Case Sources and Selection of Indicators 
4.1.1. Case Study Source 

This study selects CSDN, the most representative technical 
Q&A community in China, which was founded in 1999 and 
is currently the largest domestic UGC (User Generated 

Content) content platform in the IT field, with 31 million 
registered members, of which the Q&A community is an 
important part [19]. 

A question and its answer data are randomly selected from 
the CSDN Q&A channel, and the retrieved data contains the 
question's full formulation, as well as the number of responses 
received and the content of those responses, as shown in Table 
1. 

 
Table 1. CSDN questions and their answers 

Question 
Question 

description 
Answer 

symbol 
Answer description 

What is the best 
software to use to 
draw the structure 

of a neural 
network in a 

thesis? 
(Original Text: 

论文中神经网络

的结构图用什么

软件绘制比较

好？) 

I have to make a 
structural diagram of 
GAN for my thesis, 

and I don't know what 
software or method I 

can use to make a 
structural diagram 

that meets the 
standards of the 

thesis. 
(Original Text:论文

中要做一个 GAN 的
结构示意图，不知道

使用什么软件或是方

法做出的结构图能够

达到论文的标准。) 

𝑃  https://www.zhihu.com/question/20542936 
𝑃  Try PowerPoint, it works well. If you're on a Mac, keynote is 

free. Google docs is also free if you have access to an extranet. 
The above three are basically popular drawing tools. Remember 

to export to vector PDF, then you can use it everywhere, 
including pdfLaTeX. If you want to niche a bit, GoogleNet that 

I am using pydot & Graphviz drawing, but these things need 
more hand tuning place. 

(Original Text: 试一下 PowerPoint，很好使的。如果你用
Mac 的话，keynote 免费。如果你能翻墙，Google docs 也免
费。以上三个基本上是大众画图神器。记得导出成矢量

PDF，然后就到处可以用了，包括 pdfLaTeX。如果你想小
众一点，GoogleNet 那个图我是用 pydot+Graphviz 画的，但

是这些东西需要手调的地方多一些。) 
𝑃  Visio is good, and of course the flowcharts in WPS are fine. 

(Original Text: Visio 很香，当然 WPS 里面的流程图也可
以。) 

𝑃  Visio is available and there is also software for online 
drawing. 

(Original Text: Visio 可以，也有在线绘图的软件吧。) 
 

4.1.2. Selection of Indicators 
Sussman and Siegal (2003) [20] concluded from their 

research on the information acceptance model that the quality 
of the information itself and the reliability of the information 
source are two factors affecting users' perceived value. Based 
on this, this paper considers the factors affecting the level of 
quality of Q&A information in two dimensions: answer 
information entropy (𝐺  ), answer practicality (𝐺  ), answer 

sentiment value (𝐺 ), source reliability (𝐺 ) and originality 
(𝐺 ), as shown in Table 2. Note: In order to better reflect the 
subjective nature of user needs and the "fuzzy" nature of 
question and answer evaluation data, only five qualitative 
indicators are selected here, without considering the relatively 
simple quantitative indicators (e.g. number of answer likes, 
number of answer comments). 

 
Table 2. Answer quality indicator system 

Dimension Indicator 
Indicator 
symbol 

Indicator meaning Type of indicator 

Answers 

Answer information 
entropy 

𝐺  
The amount of information contained 

in the text. 
Benefit-based 

Answer practicality 𝐺  
The answers are implementable and 

useful. 
Benefit-based 

Answer sentiment 
value 

𝐺  
Messages with positive emotions help 
to strengthen the user's identification 

[21]. 
Benefit-based 

Respondents 

Source reliability 𝐺  
The honesty, competence, enthusiasm 

and objectivity of the respondent. 
Benefit-based 

Originality 𝐺  
Answers are the product of 

independent thinking on the part of 
the respondent. 

Benefit-based 

 
 
 
 
 



 

53 

 

4.2. Establishing a Hesitant Fuzzy Information 
Evaluation Matrix 

4.2.1. Establishing the Original Hesitation Fuzzy 
Information Evaluation Matrix 

For the qualitative evaluation indicators mentioned above, 

different evaluators have different focuses, and thus we 
choose to build the hesitation fuzzy number evaluation 
information matrix, as shown in Table 3. 

 
Table 3. Hesitant fuzzy information evaluation matrix 𝐴 𝛼  

 𝐺  𝐺  𝐺  𝐺  𝐺  
𝑃  0.5, 0.7, 0.8, 0.9  0.2, 0.5, 0.6  0.4, 0.5, 0.6  0.3, 0.5, 0.6, 0.8  0.3, 0.4, 0.6  
𝑃  0.2, 0.4, 0.6  0.2, 0.3, 0.5  0.3, 0.6, 0.7, 0.8, 0.9  0.4, 0.6, 0.7, 0.9  0.2, 0.5  
𝑃  0.1, 0.4, 0.5, 0.8  0.1, 0.4, 0.6, 0.7  0.4, 0.5, 0.7, 0.9  0.3, 0.5, 0.6, 0.9  0.2, 0.4, 0.5  
𝑃  0.3, 0.5, 0.6, 0.7  0.4, 0.6  0.3, 0.5, 0.6  0.2, 0.5, 0.6, 0.7, 0.9  0.4, 0.7  

 
Note: The elements of the HFE have been sorted in 

ascending order. 
Answer 𝑃  has good answer information entropy, but its 

answer sentiment value is average. Answer 𝑃   has good 
source reliability, but assessors differ more on its answer 
sentiment value, and its answer utility and originality are 
average. Assessors disagree more on the answer information 
entropy and answer utility ratings for answer 𝑃 , which has a 
good answer sentiment value. Answer 𝑃   has better 

originality and answer utility, but assessors differ more on its 
source reliability rating value. 

4.2.2. Complementing and Normalising the HFEs in 𝑨 
Platform decision makers tend to have a risk appetite, so 

the HFEs of varying length in the HFS are supplemented 
using fuzzy element maxima (Table 4). Considering that these 
indicators are benefit-based, there is no need to deal with the 
expanded evaluation matrix 𝐵 𝛽  , i.e. 𝐻

ℎ 𝐵 𝛽 . 
 
 

Table 4. Extended hesitant fuzzy answer evaluation information matrix 𝐵 𝛽  

 𝐺  𝐺  𝐺  𝐺  𝐺  
𝑃  0.5, 0.7, 0.8, 0.9  0.2, 0.5, 0.6, 0.6  0.4, 0.5, 0.6, 0.6, 0.6  0.3, 0.5, 0.6, 0.8, 0.8  0.3, 0.4, 0.6  
𝑃  0.2, 0.4, 0.6, 0.6  0.2, 0.3, 0.5, 0.5  0.3, 0.6, 0.7, 0.8, 0.9  0.4, 0.6, 0.7, 0.9, 0.9  0.2, 0.5, 0.5  
𝑃  0.1, 0.4, 0.5, 0.8  0.1, 0.4, 0.6, 0.7  0.4, 0.5, 0.7, 0.9, 0.9  0.3, 0.5, 0.6, 0.9, 0.9  0.2, 0.4, 0.5  
𝑃  0.3, 0.5, 0.6, 0.7  0.4, 0.6, 0.6, 0.6  0.3, 0.5, 0.6, 0.6, 0.6  0.2, 0.5, 0.6, 0.7, 0.9  0.4, 0.7, 0.7  

 
 

4.3. Indicator Assignment 
4.3.1. Assigning Indicators with Fuzzy Cross-Entropy 

The fuzzy cross-entropy array 𝑄 for the fuzzy information 

set in the case of 𝑞 2 is calculated and built using Equation 
(3), as shown in Table 5. 

 
 

Table 5. Fuzzy cross-entropy matrix of the fuzzy information set 𝑄 𝐸  

 𝐺  𝐺  𝐺  𝐺  𝐺  
𝑃  0.798 7 0.975 3 0.988 5 0.952 9 0.980 7 
𝑃  0.980 1 0.936 5 0.890 2 0.833 4 0.941 1 
𝑃  0.989 8 0.978 9 0.868 1 0.911 3 0.928 3 
𝑃  0.995 2 0.980 9 0.984 6 0.972 5 0.942 2 

 
 

The indicator weights based on the entropy measure are 
calculated according to Equation (4): 𝜔
0.202, 0.110, 0.230, 0.282, 0.177 . 

4.3.2. Adjusting Weights 
(1) Integrating HFEs 
For the information evaluation matrix 𝐴  (Table 3), the 

geometric score 𝑠 ℎ   of ℎ   is calculated using Equation 
(5), which in turn yields the geometric score matrix 𝑆. 

𝑆 𝑠 ℎ

𝐺 𝐺 𝐺 𝐺 𝐺
𝑃
𝑃
𝑃
𝑃

0.708 5 0.391 5 0.493 2
0.363 4 0.310 7 0.618 8

0.518 0 0.416 0
0.623 6 0.316 2

0.355 7 0.360 0 0.595 8
0.501 0 0.489 9 0.448 1

0.533 5 0.342 0
0.519 4 0.529 2

 

(2) Calculating the Grey Correlation between Indicators 
According to the research by Fan Kai and Wu Haoying 

(2002) [22], the corresponding 𝜌 ⌈𝜎⌉ ⌈0.579⌉  for the 
information evaluation matrix is calculated, so the 
discrimination coefficient 𝜌 0.6  is used in this work. 
Using Equations (1) and (2) to calculate the correlation degree 
between two indicators, the grey correlation matrix between 
indicators 𝐶 𝑟  is obtained, as shown in Figure 1. 

 



 

54 

 
Figure 1. Grey correlation matrix between indicators 𝐶  

 

(3) Standardising 𝐶  
Since the minimum indicator correlation 𝛾 min 𝑟

𝑟 0.530 1 , the normalised effective grey correlation 

matrix 𝐶 𝑑 𝛾 𝑟  is obtained, as shown in 

Figure 2. 
 

 
Figure 2. Effective grey correlation matrix 𝐶  

 

(4) Adjusting the weights 𝜔  
Based on 𝐶  , the corrected indicator weights 𝜔 ′′  are 

calculated using Equations (9) and (10). 
𝜔 ′′ 0.198 8, 0.083 4, 0.296 4, 0.282 9, 0.138 5  

4.4. Answer Ranking Based on Grey 
Correlation Analysis 

For 𝐻 ℎ 𝐵 𝛽  , the correlation 
coefficien 𝜂  for each ℎ  is calculated using Equation (14) 
to obtain the grey correlation coefficient  matrix 𝑁. 

𝑁 𝜂

𝐺 𝐺 𝐺 𝐺 𝐺
𝑃
𝑃
𝑃
𝑃

1.000 0 0.739 3 0.660 1
0.469 7 0.560 3 0.882 4

0.705 9 0.618 7
1.000 0 0.545 5

0.492 4 0.747 5 0.941 2
0.545 5 0.926 5 0.601 3

0.823 5 0.511 8
0.700 5 1.000 0

 

Based on 𝑁 and 𝜔 , 𝑅  is calculated using Equation (16). 
𝑅 0.741 5, 0.760 1, 0.743 1, 0.700 6  

Therefore, according to the value of 𝑅 , the comprehensive 
ranking of the alternative answers is 𝑃 𝑃 𝑃 𝑃 , and 
the best filtered answer is 𝑃 . 

4.5. Analysis of Answer Ranking Results 
Firstly, we analyze the answer 𝑃 , which is better than the 

other three alternatives in terms of textual information (𝐺  
answer information entropy), answer implementability (𝐺  
answer practicality). It is informative and shows the 
enthusiasm and honesty of the respondent ( 𝐺   source 
reliability), and such an answer can also help to enhance the 
audience's sense of identity (𝐺  answer sentiment value). 𝑃  
is ranked highly and filtered as the relatively best answer. 

Secondly, answer 𝑃  , which presented only one external 
link, was analysed; formally, the external link contains the 
content of the answer and to some extent enhances the 
credibility of the answer. However, the website link requires 
the user to jump out of the content of that answer, which to 
some extent reduces the efficiency of users in accessing 
information. Therefore, with the revised weight 𝜔 , 𝑃  does 
not have a dominant ranking. 

Again, the analysis of the lower-ranked answer 𝑃  shows 
that the information entropy of 𝑃  is relatively low compared 
to that of 𝑃 . Although the text of 𝑃  is not long, its text is a 
web link, and 𝑃   includes more information than 𝑃  . 
Compared to 𝑃 , answer 𝑃  provides a less clear solution to 
the question (recommendation of software for drawing 
structural diagrams) than 𝑃 , mentioning only "software for 
online drawing" in general terms, and is therefore the least 
recommended answer 𝑃  in the overall assessment. 

4.6. Sensitivity Analysis 
4.6.1. Analysis of the Impact before and after the 

Correction of Indicator Weights 
The grey correlation of each answer 𝑃   with the ideal 

answer 𝑃   and their ranking results before and after the 
adjustment of indicator weights are shown in Table 6. 

 
 

Table 6. Grey correlation between each answer and the ideal answer before and after the weighting adjustment and the 
ranking of answers 

Indicator weights 𝑅  𝑅  𝑅  𝑅  Ranking 
Before adjustment 0.743 7 0.738 0 0.721 0 0.724 9 𝑃 𝑃 𝑃 𝑃  
After adjustment 0.741 5 0.760 1 0.743 1 0.700 6 𝑃 𝑃 𝑃 𝑃  

 
 

As can be seen from Table 6, answer 𝑃  takes the place of 
𝑃   after the adjustment of weights and jumps to the first 
position, while answer 𝑃   is at the bottom. The correlation 
matrix 𝐶   between the indicators shows that answer 

practicality 𝐺   has a strong correlation with originality 𝐺  
(0.898 9), and answer sentiment value 𝐺   has a low 
correlation with the rest of the indicators (all less than 0.580 
0) except for a high correlation with source reliability 𝐺  



 

55 

(0.829 2), thus adjusting the weights to weaken the correlation 
between the indicators. Therefore, the final answer sentiment 
value 𝐺   weighting (0.296 4) is relatively high, and the 
answer practicality 𝐺   (0.083 4) and originality 𝐺  
weightings (0.138 5) are relatively low, allowing the answer 
ranking to be adjusted and the adjusted ranking results to be 
more reasonable and accurate. 

4.6.2. Analysis of the Effect of the HFE-Completion 
Strategy on the Results 

When platform decision makers tend to be risk averse, 
HFEs of unequal length in the fuzzy set are complemented 
using the elemental minimum of the HFE, as shown in Table 
7. 

 
Table 7. Extended hesitant fuzzy answer evaluation information matrix 𝐵′ 𝛽 ′  

 𝐺  𝐺  𝐺  𝐺  𝐺  
𝑃  0.5, 0.7, 0.8, 0.9  0.2, 0.2, 0.5, 0.6  0.4, 0.4, 0.4, 0.5, 0.6  0.3, 0.3, 0.5, 0.6, 0.8  0.3, 0.4, 0.6  
𝑃  0.2, 0.2, 0.4, 0.6  0.2, 0.2, 0.3, 0.5  0.3, 0.6, 0.7, 0.8, 0.9  0.4, 0.4, 0.6, 0.7, 0.9  0.2, 0.2, 0.5  
𝑃  0.1, 0.4, 0.5, 0.8  0.1, 0.4, 0.6, 0.7  0.4, 0.4, 0.5, 0.7, 0.9  0.3, 0.3, 0.5, 0.6, 0.9  0.2, 0.4, 0.5  
𝑃  0.3, 0.5, 0.6, 0.7  0.4, 0.4, 0.4, 0.6  0.3, 0.3, 0.3, 0.5, 0.6  0.2, 0.5, 0.6, 0.7, 0.9  0.4, 0.4, 0.7  

 
 

Based on 𝐵 , indicator weighting and answer ranking are 
performed and the results are shown in the third row of Table 

8. 

 
Table 8. Gray correlation of each answer with the ideal answer and answer ranking under different HFE completion 

strategies 
Types of risk for platform decision 

makers 
𝑅  𝑅  𝑅  𝑅  Ranking 

Risk-loving 0.741 5 0.760 1 0.743 1 0.700 6 𝑃 𝑃 𝑃 𝑃  
Risk-averse 0.787 6 0.672 8 0.724 3 0.737 9 𝑃 𝑃 𝑃 𝑃  

 
 

As can be seen from Table 8, the ranking of each alternative 
answer varies considerably when different HFE-completion 
strategies are chosen. When the platform decision maker is 
risk-loving, 𝑃   is the relatively best answer. When the 
platform decision maker is risk-averse, answer 𝑃   is 
recommended, but 𝑃  is least recommended. 

The impact of different HFE-completion strategies on 
decision making is summarised for alternative answers (i.e. 
comments) containing links to websites (two scenarios, i.e. 
unopened URL and opened URL). Firstly, changes in the 
completion strategies affect changes in the weights. Secondly, 
different types of information affect users' overall perceptions, 
and in the process of judging information quality, users 
consider textual information more important than hyperlink 
information [23]. Again, for decision makers using a risk-
loving completion strategy, it is recommended that decision 
makers choose answers with detailed textual content rather 
than open URLs. Because URL skipping reduces the user's 
efficiency in accessing information to a certain extent, risk-
loving decision makers may not click on the link to save time 
costs (risk not understanding the content behind the URL) and 
choose 𝑃  with richer text content and moderate text length 
(which can be regarded as having high sentiment value 𝐺  
and reliability 𝐺  ). For decision makers with a risk-averse 
strategy, it is recommended that decision makers choose 
answers that contain external links. Although it is more time 
consuming to jump links, the risk-averse decision maker 
clicks on the link to be on the safe side, i.e. chooses 𝑃  with 
the possibility of multiple solutions due to the page jump 
(which can be considered as a higher information entropy 𝐺 ). 

In summary, the use of modified weights allows platform 
decision-makers with different risk types to select the answer 
they want (if the decision-maker tends to be risk-loving, it is 
recommended that they select the answer that is text-rich and 
does not require opening external links; if the decision-maker 
tends to be risk-averse, it is recommended that they select the 

answer that contains external links), which also demonstrates 
the reasonableness of the weighting adjustment and the 
effectiveness of the evaluation method. 

5. Conclusion 
This study addresses the problem of varying quality of 

information in Q&A communities. Considering the 
"fuzziness" in the quantification of the answers' qualitative 
indicators, a hesitant fuzzy information evaluation matrix was 
established to reasonably quantify the qualitative indicators 
and effectively measure the differences in assessment among 
evaluators. As the evaluation matrix was already subjective, 
fuzzy cross-entropy was used to objectively assign weight to 
the indicators, and the grey correlation between indicators 
was measured to correct the weights, taking into account the 
possible overlapping information between indicators. Finally, 
based on the grey fuzzy evaluation method, the weighted grey 
correlation of the answers was obtained and the answers were 
ranked accordingly. Selected examples of questions and 
answers from CSDN were analysed, and the results show that 
the grey fuzzy evaluation method quantifies the qualitative 
indicators and can process and analyse indicators that reflect 
the subjective nature of user needs. By modifying the 
indicator weights, the homogeneous information between 
indicators was effectively weakened, making the final answer 
evaluation ranking more realistic. A sensitivity analysis was 
also conducted for the changes in the HFE-completion 
strategy to explore the rationality of the recommended 
answers. However, this paper only considers qualitative 
indicators when ranking answers, and will next consider how 
to combine qualitative indicators with quantitative indicators 
to evaluate the quality of Q&A community answers. 



 

56 

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