Party Discipline Measurement Decision-Making Based on Hesitant
Fuzzy and VIKOR Method
Honglin Shi, Xin Zhang
*
and Bin Ge
College of Systems Engineering, National University of Defense Technology, China
Keywords: Discipline Measurement, Multicriteria Group Decision-Making, Hesitant Fuzzy, Vlsekriterijumska Optimi-
zacija I Kompromisno Resenje (VIKOR) Method.
Abstract: Discipline measurement refers to the activity of determining whether and what kind of punishment should be
given to the violator based on identifying the facts of the violation and accurately determining the nature of
the violation according to the corresponding disciplinary regulations. This kind of action can be regarded as
a multicriteria group decision-making problem. At present, the grass-roots discipline inspection and supervi-
sion organs mainly use qualitative methods in the process of discussing disciplinary action, which is greatly
influenced by subjective or objective factors, and are difficult to fully absorb the opinions from groups, which
means it lacks a kind of quantitative decision-making methods. Based on the above reasons, this paper uses
linguistic variables for the first time to describe the principles of taking disciplinary action, and on this basis,
a multicriteria assisted decision-making method for discussing the disciplinary action is proposed based on
hesitant fuzzy theory and VlseKriterijumska optimizacija I kompromisno resenje (VIKOR) method, which
provides a new method for discipline measurement. It is an important auxiliary decision-making method. This
paper takes a real case as an example to prove the effectiveness of this method.
1 INTRODUCTION
Strengthening the construction of the Party's system
is an important measure to implement the strict gov-
ernance of the Party in an all-around way. Among
them, the construction of the Party's discipline, laws,
and regulations are the most important contents of the
construction of the system (Wan 2017). The imple-
mentation of Party disciplinary sanctions is an im-
portant means to maintain the authority and serious-
ness of Party regulations, and also an important link
in the supervision and enforcement of discipline by
the discipline inspection and supervision organs. Ac-
cording to the statistics informed on the website of the
CPC Central Commission for Discipline Inspection,
from 2016 to 2021, the number of people subject to
party discipline punishment was 347,000, 443,000,
526,000, 502,000, 522,000, and 524,000 respectively,
with a total of 2,864,000 people disciplined by the
Party in six years.
Due to the characteristics of discipline, the regu-
lations and criteria based on which the party discipli-
nary sanctions are not as detailed and precise as the
legal terms, making it easy for the staff of the grass-
roots disciplinary inspection and supervision organs
to be influenced by a variety of factors, such as inac-
curate policies, lack of personal experience, and the
rendering of social opinion, etc. At present, grassroots
disciplinary inspection and supervision organs
mainly use qualitative methods to make disciplinary
decisions, which lack quantitative decision-making
methods. This is a feature that is more prominent
when dealing with issues that do not yet reach the
level of expulsion from the party, which accounts for
the majority of disciplinary problems. At the same
time, the lack of specific provisions in the disciplinary
procedures is prone to the problem of irregularities in
the process of discipline. In the actual quantity disci-
pline, it is difficult to grasp the scale of quantity dis-
cipline, to effectively punish violators, play a warning
role, and not seriously attack people's enthusiasm,
thus affecting post-case governance. This kind of
pressure of measuring discipline actions sometimes
will cause discipline inspectors to be less confident in
actual work or less independent of superiors and pros-
ecutors.
Most of the existing literature on the study of dis-
ciplinary measurement is the qualitative study from
the legal or political perspective. For example, the lit-
erature (Wang 2012) studied how to standardize the
60
Shi, H., Zhang, X. and Ge, B.
Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method.
DOI: 10.5220/0012070000003624
In Proceedings of the 2nd International Conference on Public Management and Big Data Analysis (PMBDA 2022), pages 60-70
ISBN: 978-989-758-658-3
Copyright
c
2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
disciplinary procedures of disciplinary organs and
made recommendations. The literature (Shen 2016)
conducted a study on the issue of measuring disci-
pline in the enforcement of discipline by grassroots
discipline inspection and supervision organs and ana-
lyzed the current situation of the work of measuring
discipline, especially the problems and causes. The
literature (Liu 2019) conducted a study on how to
identify disciplinary violations that do not implement
disciplinary decisions by the regulations, and in doing
so, illustrated the main basis for qualitative discipli-
nary measures. The literature (Hu 2020) conducted a
study on the problem of precise discipline measure-
ment by grassroots disciplinary organs and put for-
ward the main problems, reasons, and countermeas-
ure suggestions. The literature (Fu 2021) studied the
problem of discipline measurement in a provincial
grassroots discipline inspection and supervision or-
gan, pointing out the problems in discipline measure-
ment in a provincial grassroots discipline inspection
and prosecution organ and proposing solutions. Be-
cause of the complexity and ambiguity of the factors
to be considered in measuring discipline for party dis-
cipline, it is more difficult to describe quantitatively
using precise numbers without losing information.
Therefore, despite the urgent need for a quantitative
scientific decision-making method with strong expla-
nations and a transparent process, little research has
been conducted in this area.
To describe and deal with fuzzy information,
since Zadeh proposed the concept of fuzzy sets in
1965 (Zadeh 1965), related research has developed
rapidly, and interval fuzzy sets (Turksen 1998), intu-
itionistic fuzzy sets (Atanassov 1986), and interval in-
tuitionistic fuzzy sets (Atanassov and Gargov 1989)
have been proposed successively. In 2009, Torra and
Narukawa proposed the concept of hesitant fuzzy
sets, whose basic composition is hesitant fuzzy ele-
ments, each element is a set consisting of several pos-
sible values characterizing the degree of hesitation in
the evaluation of the multiple evaluations of the solu-
tion formed simultaneously by the decision maker
(Torra 2010). Therefore, hesitation fuzzy sets can
portray hesitation information affecting decision-
makers more comprehensively and carefully than
other extended forms of fuzzy sets. In 2011, Xu
Zeshui et al. proposed a mathematical expression for
hesitation fuzzy sets, which defines the mathematical
expressions of hesitant fuzzy elements (Xia and Xu
2010). With the development of fuzzy theory, entropy
was introduced to describe the degree of fuzziness of
information, and Deluca gave the definition of fuzzy
entropy around affiliation and non-affiliation in 1972
(Deluca and Termini 1972), and later scholars con-
ducted extensive research on entropy measurement
around intuitionistic fuzzy sets and hesitation fuzzy
sets. The literature (Szmidt and Kacprzyk 2001) stud-
ied affiliation-based and distance-based probabilistic
hesitant fuzzy entropy and proposed an axiom of en-
tropy. The literature (Mei and Li 2019) proposed the
calculation method of parametric hesitant fuzzy en-
tropy, which effectively avoids the counterintuitive
situation. At present, the hesitant fuzzy theory is ap-
plied in decision-making research in various fields. In
the work of discipline measurement, disciplinary in-
spectors will take a collective study to discuss the cir-
cumstances of disciplinary violations, application of
regulations, disciplinary schemes, etc. The linguistic
variables can be used to quantify the discipline meas-
urement criteria, and then the hesitation fuzzy set can
be used to describe the different opinions so that the
group opinion can be described completely.
In 1998, Opricovi proposed the VIKOR method
(Opricovic 1998) for selecting the best solution by
maximizing group utility and minimizing individual
regret in multi-criteria decision problems with con-
flicting and non-commensurable criteria (Opricovic
and Tzeng 2004). Combining fuzzy theory with the
VIKOR method has been applied not only to prob-
lems in engineering management such as CO2 trans-
mission pipeline failure mode and impact analysis
(Narayanamoorthy et al. 2019), industrial robot selec-
tion (Guo et al. 2019), offshore tug selection (Balin et
al. 2020), marine air compressor selection (Kaya et al.
2022), project investment selection (Wang and Li
2022), and equipment supplier selection (Zhang et al.
2019), but also in sociology and biomedical fields
have been widely used (HU et al. 2020; Kirişci et al.
2022; Akram et al. 2022).
Considering the disciplinary measurement prob-
lem as a multi-criteria group decision problem, there
are two difficulties to be solved, one is how to express
the disciplinary discipline criteria described qualita-
tively in the way of quantitative language. The second
is how to build a reasonable decision model that can
follow the principle of "punishing before and after,
curing the disease and saving the others", fully inte-
grate different opinions, and form a reasonable rec-
ommendation for decision makers to choose from. To
solve these difficult problems, this paper adopts the
linguistic variables corresponding to fuzzy numbers
to quantify the disciplinary criteria for party disci-
pline and uses hesitant fuzzy sets to portray the opin-
ions of different people in the decision-making group.
Finally, the VIKOR method is used to synthesize the
opinions of the decision-making group and rank the
disciplinary scheme to form recommendations. This
Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method
61
paper proposes, for the first time, a quantitative deci-
sion aid method for party disciplinary measurement,
and verifies the effectiveness of the method through a
practical example. In Section 2, we present criteria for
disciplinary measurement. In Section 3, we introduce
the basic theories of hesitation fuzzy and VIKOR
methods. In Section 4, we propose a decision model
based on hesitation fuzzy and VIKOR methods to as-
sist the discipline measurement. Then we illustrate a
numerical example to show the efficiency of the pro-
posed method in Section 5. In Section 6, we summa-
rize the research results of this paper.
2 DISCIPLINARY CRITERIA
FOR DISCIPLINARY
MEASUREMENT
The results of the disciplinary measurement are not
only related to the personal interests of the people
concerned, but also to the maintenance of the serious-
ness and authority of the party discipline, which
should be based on the following 6 basic criteria:
(1) Circumstances of violating discipline. The cir-
cumstances of disciplinary violations are an im-
portant reference basis for measuring discipline and
the core reference for measuring the degree of mis-
takes of people who violate discipline. In analyzing
the circumstances of the violation, the nature and se-
verity of the violation should be measured. The focus
should be on "three distinctions," that is, distinguish-
ing between mistakes made by lack of experience and
deliberate acts of doing. Distinguish between explor-
atory experiments when the state has not yet ex-
pressly provided for them from regulated non-com-
pliance with acts that are expressly prohibited by the
state. Distinguish between unintentional negligence
in promoting reform and deliberate acts for personal
gain.
(2) Harmfulness. Harmfulness is a measure of the
degree of influence of disciplinary action and is a spe-
cific description of the language of "causing serious
influence" as stated in the Regulations on Party Dis-
cipline, which is an important reference in the process
of discipline. Harmfulness should be measured in
three aspects: the degree of economic loss caused, the
degree of damage to the Party's image, and the degree
of negative effects on the field.
(3) Punishment. The degree of punishment is an
important criterion to measure the disciplinary
scheme and should follow the principle of "con-
sistency of crime and punishment" in the law, not
only to achieve the purpose of discipline but also not
to reflect the strict enforcement of discipline and de-
liberately upgrade the level of punishment. The de-
gree of the subsequent impact on the person disci-
plined and the result of the discipline against similar
violations should be considered.
(4) Deterrence. To achieve the purpose of "deal-
ing with one, governing a filed", the implementation
of party discipline must form an appropriate deter-
rent, so the degree of deterrence is also one of the cri-
teria to measure the effectiveness of the disciplinary
measure. Mainly contains the degree of deterrence in
a field and the degree of warning to the violator.
(5) Regulatory matching. The Regulations on
Party Disciplinary Punishment is the core basis for
disciplinary organs to implement disciplinary punish-
ments. Because of the strong generalization of the
language, it is necessary to analyze in depth to match
the facts with the content of the regulations, and cor-
rectly determine the nature of the violation and the
punishment scheme.
(6) Other factors. The principle of disciplinary
punishment is "to punish the former to prevent the lat-
ter and to cure the sick to save the others". To avoid
the problem of generalization and simplification of
accountability and responsibility, one should consider
the violator’s consistent performance, as appropriate.
According to the above principles, a system of
disciplinary criteria for party discipline is established,
as shown in Table 1.
Table 1: The criteria of the party disciplinary action measure
Disciplinary Cri-
teria
Language Variables
Variable
Type
Variable Description
Circumstances of
violating disci-
pline
(C1)
C11 Matching degree of vio-
lation circumstances
Benefit
The matching degree of the punishment
and the severit
y
of the violation.
C12 Matching degree of atti-
tude
Benefit
The matching degree of the punishment
and the violator's attitude towards mis-
takes.
Harmfulness
(C2)
C21 Degree of punishment
for economic losses
Benefit
The matching degree of the punishment
and the economic loss caused.
PMBDA 2022 - International Conference on Public Management and Big Data Analysis
62
C22 Degree of punishment
that damages the image of the
p
art
y
Benefit
The matching degree of the punishment
and the negative impact on the image of
the party.
C23 Degree of punishment
for negative demonstration
effects
Benefit
The matching degree of punishment and
negative demonstration effect.
Punishment
(C3)
C31 Degree of punishment
for sub
j
ective intent
Benefit
The degree of punishment to the subjec-
tive intent of the violator.
C32 Subsequent impact de-
gree
Cost
The impact of the punishment on the
subsequent career development of the
violator.
C33 Similarity to similar
cases
Benefit
The degree of similarity of punishment
results com
p
ared with similar cases.
Deterrence
(C4)
C41 Deterrence to the field Benefit
The degree to which the punishment is
expected to have a warning effect on the
industr
y
.
C42 Warning degree for vio-
lators
Benefit
The degree to which the punishment is
expected to have a warning effect on the
violator.
Regulatory
matching
(
C5
)
C51 Degree of matching with
regulations
Benefit
The degree to which the punishment
matches the provisions of relevant laws
and re
g
ulations.
Other factors
(C6)
C61 Degree of matching with
the daily performance
Benefit
The matching degree of the punishment
and the consistent daily work perfor-
mance of the violator.
3 HESITANT FUZZY MULTI-
CRITERIA GROUP DECISION
MAKING METHOD
In the process of measuring discipline, different dis-
ciplinary inspectors tend to hold different opinions on
the final disciplinary scheme. In order to absorb the
different opinions from the decision-making group
completely, we use hesitant fuzzy information to de-
scribe different views quantitatively. The following
parts will introduce the basic concepts of hesitant
fuzzy sets and the method of multi-criteria group de-
cision-making.
3.1 Hesitant Fuzzy Set Theory
Definition 1 (Xia and Xu 2010). If 𝑋 is a fixed set.
Then the hesitant set is a function of each element of
𝑋 mapped to a subset of [0,1]. Mathematically, it is
represented by the following expression:
𝐴={
〈
𝑥,ℎ
(𝑥)
〉
|𝑥∈𝑋},
where ℎ
(𝑥) is the set of some values in [0,1], indi-
cating some possible affiliations of the element 𝑥
about the set 𝐴. So ℎ
(𝑥) is called the hesitant fuzzy
element. 𝛩 represents the collection of all hesitant
fuzzy elements (Xu and Xia 2011).
Definition 2 (Torra and Narukawa 2009). Let 𝐴=
{ℎ
,ℎ
,…,ℎ
} be an n-dimensional set of hesitant
fuzzy elements, 𝜗 is the hesitant fuzzy elements in-
tegration function defined on the set 𝐴, 𝜗:
[
0,1
]
→
[
0,1
]
, then we have:
𝜗
=
{𝜗
(
γ
)
}
∈{
×
×…×
}
.
The hesitant fuzzy weighted average (HFWA) op-
erator cited in this paper is the mapping Θ
𝓃
→Θ,
which can be written (Xia and Xu 2010):
𝐻𝐹𝑊𝐴
(
ℎ
,ℎ
,...,ℎ
)
=⨁
𝑤
ℎ
=
1− (1−γ
)
∈
,
∈
,...,
∈
, (1)
where 𝑤=
(
𝑤
,𝑤
,...,𝑤
)
is the weight vector of
ℎ
(
𝑖=1,2,...,𝑛
)
, 𝑤∈
[
0,1
]
, 𝑖=1,2,...,𝑛, and
∑
𝑤
=1
. In particular, if the weights of the crite-
ria are equal, 𝑤=
,
,...,
, then the HFWA op-
erator degenerates to the hesitant fuzzy average
(HFA) operator:
𝐻𝐹𝐴
(
ℎ
,ℎ
,...,ℎ
)
=
⨁
ℎ
=
1− (1−𝛾
)
.
∈
,
∈
,...,
∈
(2)
In an anonymous case, suppose the decision-
maker provides several evaluation values for scheme
𝐴
under the criterion 𝑥
, then these values can be
considered fuzzy elements ℎ
. When two decision
Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method
63
makers provide the same evaluation value, then the
value appears only once in the set consisting of ℎ
.
Definition 3 (Xu and Xia 2011). Assuming 𝐴
and
𝐴
are two hesitant fuzzy sets on 𝑋. 𝑙
(
)
and
𝑙
(
)
denote the number of elements contained in
ℎ
(𝑥
) and ℎ
(𝑥
) respectively. When 𝑙
(
)
≠
𝑙
(
)
, let 𝑙
=𝑚𝑎𝑥𝑙
(
)
,𝑙
(
)
, then its
hesitant fuzzy standard Hamming distance can be de-
fined as:
𝑑
(
𝐴
,𝐴
)
=
1
𝑛
1
𝑙
ℎ
(
)
(
𝑥
)
−ℎ
(
)
(
𝑥
)
, (3)
where ℎ
(
)
(
𝑥
)
and ℎ
(
)
(
𝑥
)
are the 𝑗th largest
values in ℎ
(𝑥
) and ℎ
(𝑥
), respectively.
In the process of calculating the distance, when
two sets of fuzzy numbers do not contain the same
number of elements, the set with fewer elements
should be expanded to make itself equal to the num-
ber of elements contained in the other set. The added
value can be one or several of the affiliations con-
tained in this hesitant fuzzy number. The specific
choice depends on the decision maker’s risk prefer-
ence. If by optimistic principle, the maximum value
is added; If by pessimistic principle, the minimum
value is added.
3.2 VIKOR Method
The core of the VIKOR method is to find compromise
solutions with the two key characteristics of maxi-
mum group utility and minimum individual regret. Its
main principle is to prioritize each solution based on
the positive ideal solution 𝑓
and the negative ideal
solution 𝑓
according to the approximation of the
evaluation value of the alternative to the ideal solu-
tion. Multicriteria measure of alternatives is devel-
oped from the 𝐿
−𝑚𝑒𝑡𝑟𝑖𝑐 distance measure of the
aggregate function,
𝐿
=
𝑤
𝑓
∗
−𝑓
(
𝑓
∗
−𝑓
)
, (4)
where, 1≤𝑝≤∞,𝑗=1,2,…,𝑚.
When each alternative 𝐴
(
𝑖=1,2,...,𝑛
)
is eval-
uated as 𝑓
by evaluation criterion 𝐶
(
𝑗=
1,2,...,𝑚
)
, the positive ideal solution 𝑓
and the
negative ideal solution 𝑓
can be written as follow:
𝑓
=max
𝑓
,𝑓
=min
𝑓
,When 𝐶
is the beneficial criterion
𝑓
=min
𝑓
,𝑓
=max
𝑓
,When 𝐶
is the cost criterion
(5)
Using the values of the group utility 𝑆
and the
individual regret 𝑅
for ranking, the solution with the
smallest 𝑆
has the maximum group utility. And the
solution with the smallest 𝑅
can satisfy the mini-
mum individual regret,
𝑆
=𝐿
,
=
∑
𝑊
, (6)
𝑅
=𝐿
,
=𝑚𝑎𝑥
𝑊
, (7)
where 𝑤
denotes the weight of the 𝑗th indicator, the
smaller the value of 𝑆
the larger the group benefit
value, and the smaller the value of 𝑅
the smaller the
individual regret value. Meanwhile, the benefit ratio
value 𝑄
is obtained for each scheme:
𝑄
=
(
∗
)
∗
+
(
)(
∗
)
∗
, (8)
where 𝑆
∗
=𝑚𝑖𝑛
{
𝑆
}
， 𝑆
=𝑚𝑎𝑥
{
𝑆
}
， 𝑅
∗
=
𝑚𝑖𝑛
{
𝑅
}
，𝑅
=𝑚𝑎𝑥
{
𝑅
}
; 𝑣 is the weight of the
maximum group utility, which in this paper takes the
value as 0.5.
Eventually, the best scheme is determined by
comparing the values of 𝑄
, 𝑆
and 𝑅
for each
scheme.
3.3 Hesitant Fuzzy Entropy Measure
In the process of disciplinary decision-making, the
weight of each criterion is not appropriate to be deter-
mined by the subjective assignment method. The hes-
itation fuzzy entropy is used to describe the degree of
the hesitation fuzzy set. The larger the hesitation
fuzzy entropy of a criterion, the fuzzier the judgment
information provided by the criterion is. And the
fuzzier one should be assigned a smaller weight. On
the contrary, it should be assigned a larger weight. In
this paper, the parameterized hesitation fuzzy infor-
mation measure is introduced as the entropy measure
of the hesitation fuzzy set.
Assuming 𝐴
=
{
〈
𝑥
,ℎ
(
𝑥
)〉
|𝑥
∈𝑋
}
is a hesitant
fuzzy set on domain 𝑋=
{
𝑥
,𝑥
,...,𝑥
}
and
ℎ
(
𝑥
)
=𝛾
,𝛾
,...,𝛾
, where 𝑙
is the number of
elements in ℎ
(
𝑥
)
, then
𝐸
𝐴
=
(
)
∑
𝑙𝑜𝑔
∑
𝛾
+
1 − 𝛾
, (9)
where 𝛼>0,𝛽∈
[
0,1
]
and 𝛼+𝛽≠2. Above for-
mula is the parameterized hesitant fuzzy information
measure, also known as, the entropy of the hesitant
fuzzy set 𝐴
.
PMBDA 2022 - International Conference on Public Management and Big Data Analysis
64
4 THE HESITANT FUZZY
MULTI-CRITERIA GROUP
DECISION MODEL BASED ON
VIKOR METHOD
The core idea of the VIKOR method is to prioritize
the items based on the positive ideal solution (PIS)
and the negative ideal solution (NIS), and then to de-
termine the closeness of each item to the positive
ideal solution based on its preference value. This
method takes into account both the maximization of
group utility and the minimization of individual re-
gret, which incorporates the subjective preferences of
decision-makers. By using this method in the process
of discipline measurement, we can better integrate the
opinions of the decision-making group and give a
more appropriate scheme.
4.1 Quantitative Language Evaluation
Information
Qualitative disciplinary criteria are often described in
language. The qualitative linguistic evaluation infor-
mation can be transformed into fuzzy numbers. The
language variable evaluation information in the deci-
sion matrix is described by a set of linguistic phrase
evaluations with 10 language evaluation granulari-
ties, and the corresponding fuzzy numbers are shown
in Table 2.
Table 2: Language variables and fuzzy numbers.
Language terms Fuzzy numbers
Extremely High/ Extremely Positive (EH/EY) 1.0
Very High/Very Positive (VH/VY) 0.9
High / Positive (H/Y) 0.8
Middle High / Middle Positive (MH/MY) 0.7
Middle (M) 0.6
Little Middle (LM) 0.5
Middle Little/Middle Negative (ML/MN) 0.4
Little / Negative (L/N) 0.3
Very Little / Very Negative (VL/VN) 0.2
Extremely Little / Extremely Negative (EL/EN) 0.1
4.2 Quantitative Discipline Decision
Model Based on VIKOR Method
Considering the fuzzy characteristics of disciplinary
criteria, the decision analysis can be carried out with
VIKOR method in the following steps:
Step 1: The hesitant fuzzy decision matrix can be
constructed by the decision-making group which usu-
ally consists of the disciplinary staff, by evaluating
the options according to each quantitative discipli-
nary criterion:
𝑅=𝑟
×
=
𝑟
𝑟
𝑟
𝑟
…𝑟
⋮𝑟
⋮⋮
𝑟
𝑟
⋱⋮
⋮𝑟
,
where 𝑟
is the set of hesitant fuzzy numbers.
The entropy matrix of the hesitation fuzzy deci-
sion matrix is first obtained using the parameter hesi-
tation fuzzy entropy to determine the weight of the
quantitative discipline criterion:
𝐸=
𝐸
𝐸
𝐸
𝐸
…𝐸
⋮𝐸
⋮⋮
𝐸
𝐸
⋱⋮
⋮𝐸
. (10)
Then the decision entropy matrix is normalized by
𝐸
=
𝐸
𝑚𝑎𝑥
{
𝐸
,𝐸
,…,𝐸
}
. (11)
The weights 𝑤
for each quantitative discipline
criterion are obtained:
𝑊
=
∑∑
, (12)
where i=1,2…,𝑚; 𝑗=1,2…,𝑛.
Step 2: the positive ideal solution 𝑓
and the neg-
ative ideal solution 𝑓
are determined based on the
decision matrix.
Step 3: 𝑄
, 𝑆
and 𝑅
values are calculated for
each scheme.
𝑆
=𝐿
,
=𝑊
𝑑𝑓
−𝑓
𝑑𝑓
−𝑓
, (13)
Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method
65
𝑅
=𝐿
,
=𝑚𝑎𝑥
𝑊
, (14)
Step 4: Determine the ranking of alternatives and
trade-offs: The alternatives to be decided are ranked
according to the order of 𝑄
, 𝑆
and 𝑅
values from
smallest to largest, and the object to be evaluated is
ranked first. The smaller the value of 𝑄
, the better
the solution to be decided.
①Acceptable advantageous conditions:
𝑄
(
𝑌
)
−𝑄
(
𝑌
)
≥1∕
(
𝑛−1
)
,
where Y
is the best evaluation object in Q
ranking,
Y
is the second best evaluation object in Q
ranking,
and n is the number of alternatives.
②Acceptable stability condition: 𝑌
is the opti-
mal solution in the ranking of 𝑆
and 𝑅
.
If the condition ① is not satisfied, the maximum
value of 𝑛 satisfying 𝑄
(
𝑌
)
−𝑄
(
𝑌
)
<1∕
(
𝑛−1
)
is calculated, and the schemes 𝑌
,𝑌
,…,𝑌
are all op-
timal. If the condition ② is not satisfied, then 𝑌
，
𝑌
are optimal solutions, and the overall decision pro-
cess is shown in Figure 1.
Construct the hesitant fuzzy decision matrix.
Calculate weights of the criteria by using the
entropy method
Determine PIS and NIS values
Compute the group untility values( ), individual regret
values( ) and index values( )
Rank the alternatives sorting by P,R and Q values in the
descending order
Q
i
i
S
i
R
Figure 1: Calculation procedure of the proposed method. (Drawn by author)
5 NUMERICAL EXAMPLE
After review and investigation, a person's disciplinary
fact is as follows: violation of the private "small treas-
ury" and the use of "small treasury" money travel is-
sues. A company donated 100,000 yuan of sponsor-
ship money to the village collective set up as a "small
treasury", and use 100,000 yuan of "small treasury"
money to organize 8 village cadres and their families,
a total of 16 people to Hong Kong, Macau and other
places to travel. The comrade during the review and
investigation, the attitude of admitting mistakes is
good.
Party Discipline Measurement
C1-
Circumstances of
violating discipline
C2-
Harmfulness
C3-
Punishment
C4-
Deterrence
C5-
Regulatory
matching
C6-
Other factors
C11 C12 C21 C22 C23 C31 C32 C33 C41 C42 C51 C61
A1-Scheme A2-Scheme A3-Scheme
Figure 2: The criteria of the party discipline measurement. (Drawn by author).
In response to the disciplinary facts, the investiga-
tion team carefully considered and identified three al-
ternative disciplinary options, namely A1: warning
within the Party; A2: serious warning within the
Party; and A3: revocation of Party position. Four ex-
perts gave the decision matrix as shown in Table 3 -
Table 8 below.
PMBDA 2022 - International Conference on Public Management and Big Data Analysis
66
Table 3: Options are evaluated according to circumstances of violating discipline.
Circumstances of
violating
disci
p
line
Matching degree of
violation circumstances
Matching degree of
Attitude
A1
{
0.5,0.6
}
{
0.3,0.4
}
A2 {0.8,0.9} {0.5,0.7}
A3
{
0.3,0.5
}
{
0.3,0.5
}
According to Equation (1) and (2), the fuzzy ele-
ment ℎ
(i=1,2) of 𝐴
(
𝑖=1,2,3
)
is obtained by us-
ing HFWA operator.
𝐻𝐹𝑊𝐴
(
𝑐
,𝑐
)
=𝐻𝐹𝐴
(
𝑐
,𝑐
)
=
1
2
⨁
ℎ
1 − (1 − 𝛾
)
∈
,
∈
=
{
0.4084,0.4523,0.4708,0.5101
}
Similarly, the remaining fuzzy element aggrega-
tion results are shown in Table 9.
Table 4: Options are evaluated according to the degree of harmfulness.
Harmfulness
Degree of
punishment for eco-
nomic losses
Degree of
punishment that dam-
ages the image of the
Party
Degree of punishment
for negative demon-
stration
effects
A1 {0.3,0.6} {0.2,0.3} {0.3,0.4}
A2
{
0.6,0.8
}
{
0.7,0.9
}
{
0.7,0.9
}
A3 {0.7,0.9} {0.8,0.9} {0.8,0.9}
Table 5: Options are evaluated according to the degree of punishment.
Punishment
Degree of
punishment for
subjective intent
Subsequent
impact degree
Similarity to similar cases
A1
{
0.5,0.7
}
{
0.2,0.3
}
{
0.1,0.2
}
A2
{
0.7,0.9
}
{
0.6,0.8
}
{
0.5,0.8
}
A3 {0.8,0.9} {0.8,1.0} {0.4,0.6}
Table 6: Options are evaluated according to the degree of deterrence.
Deterrence Deterrence to the field Warning degree for violators
A1
{
0.2,0.3
}
{
0.1,0.2
}
A2 {0.6,0.8} {0.5,0.8}
A3
{
0.8,1.0
}
{
0.4,0.6
}
Table 7: Options are evaluated according to the degree of regulatory matching.
Regulatory matching Degree of matching with regulations
A1 {0.2,0.3}
A2 {0.2,0.3}
A3 {0.2,0.3}
Table 8: Options are evaluated according to other factors.
Other factors
Degree of matching with the daily
p
erformance
A1 {0.3,0.4}
A2 {0.6,0.8}
A3 {0.5,0.6}
Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method
67
Step 1: Aggregates the sub-criteria information of
each criterion using the hesitation fuzzy HFWA op-
erator, i.e., the hesitation fuzzy decision matrix is ob-
tained, as shown in Table 9.
Table 9: Aggregate values for each scheme under the discipline criterion.
A1 A2 A3
Circumstances
of violating dis-
ci
p
line
{0.4084,0.4523,
0.4708,0.5101}
{0.6838,0.7551,
0.7764,0.8268}
{0.3000,0.4084,
0.4084,0.5000}
Harmfulness
{0.5573,0.6571,
0.5901,0.6825,
0.5859,0.6792,
0.6266,0.7030,
0.6653,0.7408,
0.6902,0.7600,
0.6870,0.7575,
0.7102,0.7756
}
{0.8961,0.9400,
0.9400,0.9654,
0.9400,0.9654,
0.9800,0.9265,
0.9576,0.9755,
0.9576,0.9755,
0.9576,0.9756,
0.9755,0.9859
}
{0.9510,0.9654,
0.9654,0.9755,
0.9654,0.9755,
0.9755,0.9827,
0.9717,0.9800,
0.9800,0.9859,
0.9800,0.9859,
0.9859,0.9900
}
Punishment
{0.1515,0.2000,
0.2063,0.2517}
{0.5528,0.7172,
0.6838,0.8000}
{0.6536,0.7172，
1.0000,1.0000
}
Deterrence
{0.1515,0.2063,
0.2517,0.3000,
0.3072,0.3519}
{0.6000,0.7172,
0.6536,0.7551}
{0.8268,1.0000,
0.9000,1.0000}
Regulatory
matching
{0.2000,0.3000} {0.6000,0.8000} {0.6000,0.8000}
Other factors
{
0.3000,0.4000
}
{
0.6000,0.8000
}
{
0.5000,0.6000
}
Step 2: Using Equation (9), the entropy of the de-
cision matrix parameters is calculated. Taking 𝛼=
0.2，𝛽=1, we get:
𝐸
𝐴
=
2
𝑛
𝑙𝑜𝑔
1
𝑙
𝛾
+1−𝛾
.
The entropy matrix 𝐸 of the decision matrix is
obtained:
𝐸=
0.9983 0.9965 0.9736 0.9577 0.9560 0.9846
0.9516 0.8495 0.8725 0.9768 0.9657 0.9657
0.9913 0.7974 0.4918 0.4996
0.9657 0.9971
.
Step 3: The weight of each criterions are obtained:
𝑊
=0.18, 𝑊
=0.16, 𝑊
=0.14, 𝑊
=0.15,
𝑊
=0.18, 𝑊
=0.18.
Step 4: Determine the positive ideal solution and
negative ideal solution for each indicator:
𝑓
=
{
0.9,0.7,0.9,0.9,0.9,0.9,0.2,0.8,0.9,0.9,0.8,0.8
}
,
𝑓
=
{
0.3,0.3,0.3,0.2,0.3,0.5,1.0,0.1,0.1,0.2,0.2,0.3
}
.
Step 5: Makes the trade-off coefficient 0.5 and
calculates the group benefit value 𝑆
, the individual
regret value 𝑅
and the combined evaluation value
𝑄
, as shown in Table 10.
Table 10. Group benefit value, individual regret value and
comprehensive evaluation value
𝑆
𝑅
𝑄
A1 1.79 0.52 1.00
A2 0.48 0.09 0
A3 0.67 0.15 0.14
Step 6: Ranking selection of the solutions. By ver-
ifying the dominance criterion of acceptability and
the stability criterion of acceptability, we get
𝑄
(
𝐴
)
−𝑄
(
𝐴
)
≤𝐷𝑄，𝑄
(
𝐴
)
−𝑄
(
𝐴
)
≥𝐷𝑄, that
is, scheme A2 and scheme A3 do not satisfy the dom-
inance criterion of acceptability but scheme A2 satis-
fies the acceptability stability criterion, then both
schemes A2 and A3 are optimal, i.e., the sanctioned
person should be given a serious warning within the
Party or be given a penalty of revocation of Party po-
sition. In the actual processing of the case, the disci-
pline inspection and supervision authority gave the
sanctioned person a serious warning within the Party.
6 CONCLUSIONS
This paper proposes an auxiliary decision-making
method based on the hesitation fuzzy sum method for
party discipline disciplinary measure, which adopts a
hesitation fuzzy set to quantify the decision group
opinion, adopts an objective weighting method for the
weight of each disciplinary measure criterion, com-
bines the method to maximize group utility and min-
imize individual regret value, and then provides an
auxiliary decision-making scheme. The method, as an
auxiliary decision-making method, provides quantita-
tive tools for disciplinary measures based on the tra-
ditional qualitative method, standardizes the process
PMBDA 2022 - International Conference on Public Management and Big Data Analysis
68
of disciplinary measures, and provides a powerful
tool for the grassroots discipline inspection and su-
pervision organs in grasping the scale of disciplinary
measures, and also provides a more interpretable way
for the disciplinary measures of party discipline. At
the same time, the use of a hesitation fuzzy set can
more comprehensively portray the different opinions
of those involved in decision-making, providing a
practical tool for giving full play to the role of deci-
sion-making groups in the disciplinary work, facili-
tating further standardization of the procedure of
party disciplinary punishment and discipline, which
is of great significance for promoting the construction
of the rule of law. This paper verifies the effective-
ness of the method in the context of actual case pro-
cessing.
Through the case study, it can be found that this
method provides program recommendations for dis-
ciplinary decision-making, and decision-makers can
then choose among the recommended programs, and
the whole process also fully reflects the democratic
and centralized decision-making process, which ap-
plies to the disciplinary process of party disciplinary
punishment.
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