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

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

 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

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

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

C22 Degree of punishment

that damages the image of the

art

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

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

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

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

(

)

C51 Degree of matching with

regulations

Benefit

The degree to which the punishment

matches the provisions of relevant laws

and re

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

(

)

}

∈{



×



×…×



}

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







. 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

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





=𝑚𝑎𝑥𝑙







(



)

,𝑙







(



)

 , then its

hesitant fuzzy standard Hamming distance can be de-

fined as:

𝑑



(

𝐴



,𝐴



)

𝑛



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

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



𝑑𝑓





−𝑓





𝑑𝑓





−𝑓











, (13)

Party Discipline Measurement Decision-Making Based on Hesitant Fuzzy and VIKOR Method

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,



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

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

Table 3: Options are evaluated according to circumstances of violating discipline.

Circumstances of

violating

disci

line

Matching degree of

violation circumstances

Matching degree of

Attitude

{

0.5,0.6

}

{

0.3,0.4

}

A2 {0.8,0.9} {0.5,0.7}

{

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



)

⨁





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}

{

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

{

0.5,0.7

}

{

0.2,0.3

}

{

0.1,0.2

}

{

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

{

0.2,0.3

}

{

0.1,0.2

}

A2 {0.6,0.8} {0.5,0.8}

{

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

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

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-

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,

0.9800,0.9265,

0.9576,0.9755,

0.9576,0.9756,

0.9755,0.9859

}

{0.9510,0.9654,

0.9654,0.9755,

0.9755,0.9827,

0.9717,0.9800,

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



=

𝑛

𝑙𝑜𝑔





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

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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