Evaluation of Family Property Insurance Companies based on
Probabilistic Linguistic Almost Stochastic Dominance Criterion
Suqiong Hu
a
and Na Zhao
School of Management Science and Engineering, Shandong Technology and Business University, Yantai, Shandong, China
Keywords: Insurance Companies, Probabilistic Linguistic Term Sets, Probabilistic Linguistic Entropy Weighting
Method, Almost Stochastic Dominance Criterion.
Abstract: Family property insurance provides consumers with timely financial compensation for property losses, and
the evaluation of family property insurance companies is beneficial to consumers in choosing the right
insurance company for themselves. The evaluation index system of consumer family property insurance
companies is constructed, and the probabilistic linguistic entropy weighting method is applied to assign
objective weights to the indexes. The probabilistic linguistic almost stochastic dominance evaluation method
is proposed to calculate the utility value of family property insurance companies and obtain the strength
ranking of family property insurance companies. The evaluation results are analyzed to provide consumers
with strategies for choosing family property insurance companies under different situations and provide
theoretical suggestions for the future development direction of family property insurance companies.
1 INTRODUCTION
According to statistics from the work report of the
Supreme People’s Procuratorate of the People’s
Republic of China, in 2020 burglary and other
multiple criminal cases of property invasion, the
prosecution of up to 350,000 people, the annual
household losses caused by burglary up to 1,130
billion yuan, 450 million households can not be
guaranteed the safety of household property. In the
first quarter of 2021, a total of 176,000 fires were
reported nationwide, of which 320 deaths in urban
and rural residential fires, accounting for 82.1% of
the total number of deaths in building fires,
and 44.6%
of residential fires were fires caused by various types
of household appliances and electrical wiring,
resulting in larger direct economic losses. In order to
cope with various hazards that may occur in the home
such as burglary, fire, burst plumbing pipes, etc.,
family property insurance can give families a certain
amount of financial compensation to make up for the
large economic losses caused by sudden disasters and
reduce the burden of family property. In recent years,
due to the frequent occurrence of fire, burglary, gas
explosion, etc., people’s awareness of family
a
https://orcid.org/0000-0003-1015-3126
property insurance is gradually increasing. Overall,
the share of family property insurance held in China
is still very low in the insurance market, but with the
increase of China’s population, people’s living
standard and consumption level, the public pays more
and more attention to the allocation of family
property insurance, and the share of family property
insurance and the proportion of family property
insurance to property and casualty insurance
increases year by year. in 2015, China's family
property insurance premium income was 4.1 billion
yuan, and the premium income of family property
insurance has reached 9.1 billion yuan by 2020,
which has more than tripled, and China’s family
property insurance has been developed in recent years
from the scale alone.
At present, domestic and foreign scholars have
mainly studied family property insurance from the
macro level, mainly focusing on the factors
influencing consumers’ demand for family property
insurance, the supply and institutional design of
family property insurance market, the development
model and development dilemma of family property
insurance, etc. Few scholars have studied the choice
of family property insurance companies from the
perspective of consumers. In terms of the factors
Hu, S. and Zhao, N.
Evaluation of Family Property Insurance Companies based on Probabilistic Linguistic Almost Stochastic Dominance Criterion.
DOI: 10.5220/0011155600003440
In Proceedings of the International Conference on Big Data Economy and Digital Management (BDEDM 2022), pages 23-32
ISBN: 978-989-758-593-7
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
23

influencing consumers’ demand for family property
insurance, the characteristics of “low probability and
high loss” of sudden disasters affect consumers’ risk
perception. Using a large sample of micro-household
data, (Huang 2013) found that different households
have different levels of risk-taking in response to
disasters, resulting in different levels of household
property insurance holdings. In terms of family
property insurance market supply, (Li 2018) found
that the low level of recognition of family property
insurance is caused by the unclear positioning of
family property insurance products themselves, the
lack of abundant additional clauses, the unreasonable
rate design, and the single means of promotion. (Qi
2014) conducted an empirical analysis of survey data
and verified that perceived risk factors such as time
risk, functional risk, financial risk, and social risk and
insurance demand were significantly and negatively
correlated. The research on family property insurance
system mainly includes the determination of product
rates, the exploration of family property risks and the
design of corresponding insurance schemes. Foreign
family property insurance has certain advantages in
terms of institutional design. (İmrohoroğlu, Zhao
2018), using an equilibrium model, found that
between 1980 and 2010, the risks faced by the elderly
and the one-child policy in China led to a decline in
the number of people purchasing family property
insurance, which may account for about half of the
increase in the savings rate. In a study of Progressive
Insurance Company in the U.S., (Zhang 2020)
reported that bundling family property insurance with
auto insurance would add 5-7 years to the life cycle
of customers and insurers. Drawing on relevant
concepts that have matured abroad, many domestic
scholars have researched and found that the dilemma
of China’s family property insurance development
model is mainly manifested in two aspects:
insufficient product design and innovative channel
marketing. (Zhang 2020) suggested the integration
and development of blockchain technology with
insurance to break through the development dilemma
of family property insurance. (Zhang 2019) proposed
the idea of combining family property insurance with
other types of insurance such as auto insurance, travel
insurance, livelihood insurance, smart home and
family members insurance. On the whole, the current
domestic and foreign scholars’ research on family
property insurance mainly explores several aspects of
family property insurance, such as demand
influencing factors, system design and rate design,
dilemmas faced and corresponding enhancement
measures from the perspective of managers, and no
scholars have yet studied the choice of family
property insurance companies from the perspective of
consumer demand. Therefore, this paper firstly
constructs the evaluation index system of family
property insurance companies from the perspective of
consumers, proposes a probabilistic linguistic almost
stochastic dominance evaluation model, and uses this
model to evaluate family property insurance
companies and provide consumers with strategies to
choose family property insurance companies under
different situations.
2 CONSTRUCTION OF
EVALUATION INDICATORS
2.1 Complete Indicator System
When choosing an insurance company, consumers
need to select the company that matches their needs
in order to best meet their needs. On-demand
matching not only reduces the time and cost of
product selection and transaction for consumers, but
also improves their overall economic efficiency.
Therefore, consumer needs need to be taken into
account in the evaluation of family property
insurance companies. Based on the above research,
we found that two aspects, the quality of family
property insurance products and the strength of the
insurance company itself, have a major impact on
consumer demand. Therefore, this paper constructs
an index system for evaluating family property
insurance companies from two aspects, namely, the
quality of family property insurance products and the
comprehensive strength of family property insurance
companies, from the consumer’s perspective. By
means of literature, this paper obtains the factors that
affect consumers’ demand for family property
insurance companies.
2.1.1 Factors Influencing Consumer
Demand for Family Property
Insurance Products
It is found that factors such as rates, contracted
coverage, and definition of contracted liability of
family property insurance products influence
consumers’ demand for family property insurance
products. Meanwhile, drawing on the design
principles of family property insurance by large
insurance companies in the market, this paper adds
factors such as online sales, offline sales, additional
insurance, and coverage status that affect consumers’
demand for family property insurance products. This
paper upholds the principles of scientific, systematic,
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24

typical and operable, and uses the five dimensions of
service quality theory as the principle of index
selection, and selects nine indicators that affect
consumers’ demand for family property insurance
products, as shown in Table 1.
Table 1: Factors influencing consumer demand for family
property insurance products.
Primary
Indicators
Secondary
indicators
Five Dimensions
Product
positioning
C1 Additional
coverage
Tangibility
C2 Coverage Guaranteed
C3 Sum insured
status
Tangibility
C4 Reasonableness
of the insured
amount of time
Reliability
C5 Reasonableness
of premiu
m
Tangibility
C6 Claims
settlement
Reliability
C7 Clarity of
liabilit
y
definition
Empathy
C8 Internet sales Responsiveness
C9 Off-line sales Responsiveness
2.1.2 Factors Influencing Consumer
Demand for Family Property
Insurance Companies.
Drawing on the service quality evaluation indexes of
China’s insurance industry (Feng 2017) and the
evaluation indexes of insurance companies’ claims
service quality (Huang 2009), this paper uses the five-
dimensional theory as the principle of index selection
and the whole process of consumers’ insurance
purchase as the main line, and selects 21 more
important indexes covering the process from
insurance purchase to claims service that affect
consumers’ demand for insurance companies, as
shown in Table 2.
Table 2: Factors influencing consumer demand for family
property insurance companies.
Primary
Indicators
Secondary indicators Five Dimensions
Show work C10 Clean and tidy
store environmen
t
Tangibility
C11 Staff service
etiquette standard
situation
Tangibility
C12 Staff dressing
decently
Guaranteed
C13 Company
reimbursement
situation
Reliability
C14 Company
credibility
Reliability
Claims work C15 Insurance
network situation
Guaranteed
C16 Company’s
claims
Responsiveness
C17 Professionalism
of surveyors
Reliability
C18 Accuracy of loss
determination
Reliability
C19 Accuracy of
damage verification
Reliability
C20 Simplicity of
claim documents
Guaranteed
C21 Professionalism
of adjusting process
Reliability
Service
Timeliness
C22 Timeliness of
claims service
Responsiveness
C23 Quality of
complaint handling
Tangibility
C24 Callback during
the hesitation period
Empathy
C25 Inbound
telephone call manual
connection
Empathy
C26 Timely
processing of
complaints
Responsiveness
2.2 Indicator Selection
This section must be in one column. Since consumers
consider a large number of factors when choosing a
family property insurance company, in order to
ensure the importance and typicality among the
influencing factors, this paper will conduct a
correlation analysis, aiming to eliminate redundant
indicators.
In order to eliminate redundant indicators,
correlation analysis was conducted for each factor of
product positioning. It is generally believed that the
absolute value of Spearman coefficient is greater than
0.8, then there is a strong correlation between two
factors. In this paper, the Spearman coefficient
between two two factors is calculated by using a one-
sided test. From the calculation results, we know that
the nine factors in the product positioning correlation
analysis, the seven factors in the claims work, and the
five factors in the service timeliness become
insignificantly correlated with each other, so no
indicator is deleted.
The correlation analysis of the factors of the
presentation was conducted as shown in Table 3. The
Spearman coefficient of ‘‘Staff dressing decently’’
and ‘‘company reimbursement situation’’ is 0.827,
which means that there is a strong and significant
correlation between these two factors. Therefore, the
indicator of “Staff dressing decently” is deleted.
Evaluation of Family Property Insurance Companies based on Probabilistic Linguistic Almost Stochastic Dominance Criterion
25

Table 3: Factors influencing consumer demand for family property insurance products.
C10 C11 C12 C13 C14
C10 1
0.141 0.049 0 0.144
C11 -0.141
1 .715* 0.519 0.476
C12 -0.049
.715* 1 .827** 0.154
C13 0
0.519 .827** 1 0.048
C14 -0.144
0.476 0.154 0.048 1
**. The correlation is significant at a confidence level (one-sided) of 0.01. *. At a confidence level (one-sided) of 0.05, the correlation is significant.
The above influencing factors are sorted out and
summarized to establish the evaluation index system
of family property insurance company from the
perspective of consumers, as shown in Figure 1.
Evaluation
index system
of family
property
insur ance
company from
consumer
perspective
Product
positioning
Show W ork
Claims Work
Service
Timeliness
Additional coverage
Coverage
Sum insured status
Reasonableness of the insured amount of time
Reasonableness of premium
Clarity of liability definition
Clean and tidy store en vironment
Company credibility
Professionalism of surveyors
Claims settlement
Off-line sales
Internet sales
Staff service etiquette standard situation
Company reimbursement situation
Insurance network situation
Company’s claims
Accuracy of loss determination
Accuracy of damage verification
Simplicity of claim docum ents
Professionalism of adjusting process
Timeliness of claims service
Quality of complaint handling
Callback during the hesitation period
Inbound telep hone call manual connection
Timely processing of complaints
Figure 1: Evaluation index system of family property insurance company from consumer perspective.
3 ESTABLISHMENT OF
EVALUATION MODEL
3.1 Determination of Indicator Weights
A questionnaire survey was administered to
consumers who had purchased family property
insurance to obtain information on consumers’
linguistic evaluations of family property insurance
companies. Since the probabilistic linguistic term set
can not only describe the linguistic evaluation
information provided by the group, but also portray
the probability of the occurrence of these linguistic
information. Therefore, this paper uses the
probabilistic linguistic term set to comprehensively
and accurately describe the consumer group’s
evaluation information about family property
insurance companies.
In order to better allow decision makers to express
decision information, the definition of a probabilistic
linguistic term set is introduced.
Definition 1 (Pang 2016) Let
{
}
01
, ,...,
t
Sss s=
be an ordered set of linguistic terms, where BB
()
0,1,...,
i
s
it=
is a linguistic term and
t
is an
even number, then the probabilistic linguistic term set
PLTS
can be defined as
BDEDM 2022 - The International Conference on Big Data Economy and Digital Management
26

() ( )
{
, 0 1, 1, 2, ...,
kk k k
Lp L p L S p k=∈≤≤=
()
()
}
#
1
#, 1
Lp
k
k
Lp p
=
≤

(1)
where
k
L
denotes the
k
th linguistic term item in
()
Lp
,
k
p
denotes the probability of occurrence of
the linguistic term
k
L
, and
()
# Lp
is the number of
linguistic terms in
()
Lp
. When
()
#
1
1
Lp
k
k
p
=

＜
, it
indicates that the probabilistic information of some
linguistic terms is missing. For this reason, (Pang,
2016) proposed a method to standardize the
probabilistic information.
Definition 2 (Pang 2016) Let
()
Lp
be a
probabilistic linguistic term set with partially missing
probabilistic information, then the normalized
probabilistic linguistic term set
()
Lp
is defined as
()
()
()
{
#
1
,/ ,
Lp
kk k k
kk
k
Lp L p L Sp p p
=
=∈=

()
}
1,2,...,# .kLp=
(2)
Example 1 Let
{
0123
:,:,:,:,S s verybad s bad s medium s good=
}
4
:
s
verygood
be
a linguistic terminology set. Suppose 20 consumers
evaluate an insurance company's additional insurance
index based on this linguistic terminology set, 3
people rate it as “very poor”, 4 people rate it
as “poor”,
2 people rate it as “fair”, 6 people rate it as “good”,
and 5 people rate it as “very good”. Three people gave
the rating “very poor”, four people gave the rating
“poor”, two people gave the rating “fair”, six people
gave the rating “good”, and five people gave the
rating “very good”. At this point, the probabilistic
linguistic term set
() () () ()
{
0.15 , 0.2 , 0.1 , 0.3 ,verybad bad medium good very
()
}
0. 25good
can be used to represent the information
about the 20 consumers’ evaluation of the insurance
company’s additional insurance indicators.
The evaluation problem of family property
insurance companies studied in this paper is a multi-
indicator evaluation problem described as follows:
{
}
12
, ,...,
n
AAA A=
is assumed to be a set consisting
of family property insurance companies,
{
}
01
, ,...,
t
Sss s=
is a linguistic term set,
{
}
12
, ,...,
m
CCC C=
is an evaluation indicator set, and
the indicator weights are completely unknown. 100
consumers who have purchased family property
insurance products are invited to evaluate the family
property insurance company
i
A
based on the
linguistic term set
S
, and the evaluation indicators
j
C
considered are the evaluation indicators
established in Chapter 2. In this way, based on the
definition of the probabilistic linguistic term set, the
probabilistic linguistic term set
()
ij ij
L
p
can be
used to represent the evaluation information of 100
consumers for the family property insurance
company
i
A
under the indicator
j
C
.
In the evaluation process of family property
insurance companies, the weights of each indicator
will have an important impact on the evaluation
results. In this paper, the entropy measure of
probabilistic linguistic term sets will be used to
objectively assign weights to each evaluation index.
First, the theory about the entropy measure of
probabilistic linguistic term sets is as follows.
Definition 3 (Liu 2014) Let
() ( )
{
1, 2,
kk
Lp L p k==
()
}
...,#
L
p
be a probabilistic linguistic term set, then
define its fuzzy entropy
()
()
F
L
p θ
as
()
()
[
()
#
1
1
ln
ln 2
Lp
F
kk k
k
Lp p θαα
=
=− +

()()
1ln1
kk
αα −−


(3)
where
() ()
/ , 1, 2,..., #
kk
I
Ltk Lp α ==
. Here
()
k
I
L
,
is the subscript for the linguistic term item
k
L
.
Definition 4 [14] Let
() ( )
{
1, 2,
kk
Lp L p k==
()
}
...,#
L
p
be a probabilistic linguistic term set, then
define its hesitation entropy
()
()
H
L
p θ
as
()
()
()
()()
()
()
##
11
#2
4,
#1
0,
Lp Lp
ij ij
iji
H
Lp
pp f
Lp
Lp
==+

≥
××

=

=



γ
θ
(4)
where
()
, , 1,2,...,#
ij i j
ij Lp γαα =− =
,
i
α
and
j
α
are shown in Definition 3,
()
2/1
ij ij ij
f
γγγ
=+
.
The fuzzy entropy and hesitation entropy measure
the fuzziness and hesitation of the probabilistic
linguistic term set, respectively, and they reflect the
degree of uncertainty of the probabilistic linguistic
term set from different perspectives. On this basis, the
total entropy of the set of probabilistic linguistic
terms is defined as follows.
Definition 5 (Liu 2018) Let
() ( )
{
1, 2,
kk
Lp L p k==
()
}
...,#
L
p
be a probabilistic linguistic term set, then
its total entropy
()
()
T
L
p θ
is defined as
Evaluation of Family Property Insurance Companies based on Probabilistic Linguistic Almost Stochastic Dominance Criterion
27

()
()
()
()
()
()
TFH
L
pLpLp θθθ =+
()
()
()
()
FH
L
pLp θθ −×
(5)
where
()
()
F
L
p θ
is the fuzzy entropy of
()
Lp
,
()
()
H
L
p θ
is the hesitant entropy of
()
Lp
.
From the information entropy theory, it is known
that for a certain index, the greater the entropy value
of the evaluation information, the greater the
uncertainty contained in the evaluation information,
and therefore assign a smaller weight to the index;
conversely, the smaller the entropy value, assign a
larger weight to the index. In view of this, the weights
j
w
of evaluation indicators
j
C
are defined as
follows.
()
()
()
()
()
()
1
11
1
,1,2,...,
1
n
T
ij ij
i
j
mn
T
ij ij
ji
Lp
wjm
Lp
θ
θ
=
==
−
==
−


(6)
3.2 Model Establishment
In the evaluation process of family property insurance
companies, insurance products are usually ranked
comparatively. almost stochastic dominance provides
the theoretical basis for the ranking of the options.
almost stochastic dominance, which refers to
comparing the distribution functions of two different
random variables, stipulates that as long as most
decision makers think that the insurance product
1
A
dominates
2
A
, it is not necessary for all decision
makers to make the same decision, eliminating
extreme and unrealistic utility functions, and thus
more consistent with actual decision making, so
based on the traditional almost stochastic dominance
criterion (Leshno, Levy 2002), this paper proposes an
almost stochastic dominance evaluation method
applicable to the probabilistic linguistic environment.
According to almost stochastic dominance theory.
Definition 6 (Leshno, Levy 2002) Suppose
X
and
Y
are random variables on
[
]
,ab
,
()
F
x
and
()
Gx
are the cumulative distribution functions of
X
and
Y
, respectively,
()
F
E
x
and
()
G
E
x
are
the expectations of
X
and
Y
, respectively,
u
is
the utility function of the decision maker, and
()
F
E
ux
and
()
G
E
ux
are the expectations of the
utility functions of
X
and
Y
, respectively; for any
0.5 1 ε <<
,
()
almost
U ε
denotes the other utility
functions that exclude the extreme utility functions of
set. Then
X
almostly randomly prevails over
Y
when and only when for any
()
almost
uU ε ∈
, there
() ()
FG
E
ux Eux≥
holds, where
() () () ()
{
}
{
()
'0,'inf' 1/
almost
U uux ux ux εε =≥≤ 

]
[
]
}
1, ,
x
ab−∀∈
.
In the evaluation process of family property
insurance companies, decision members hold
different decision attitudes toward insurance products
in the actual decision making due to their different
experiences and cognitive levels, and the variability
of decision attitudes leads to different decision
results. For this reason, the decision making attitudes
of decision makers need to be considered in the
decision making process. In this paper, we consider
two types of decision making attitudes: pessimistic
and optimistic attitudes. The decision maker with
optimistic attitude is more bold and aggressive, and
tends to choose larger elements, while the decision
maker with pessimistic attitude is more cautious and
tends to choose smaller elements.
The utility function is a measure of the change in
the decision maker’s preference or aversion to the
consequences of the decision when faced with a risky
situation, and the concept of probabilistic linguistic
utility function is given below based on the decision
maker’s attitude.
Definition 7 Let
() ( ) ()
{
}
1, 2,..., #
kk
L
pLpk Lp==
be
a set of probabilistic linguistic terms and define the
probabilistic linguistic utility function
()
()
uLp
when the decision maker is an optimist as
()
()
()
()
()
0
,
k
t
kk
IL
uLp IL p ϕ
=
=

(7)
where
()
()
() ()
()
() ()
min
,0
2
,,
22
,
max 2
k
kk
k
kk k k
k
kk
k
p
t
IL IL
p
tt
IL p p IL
p
t
I
LILt
p
ϕ

×≤



=× =



×≤


＜
＜
Definition 8 Let
() ( ) ()
{
}
1, 2,...,#
kk
L
pLpk Lp==
be a set of probabilistic linguistic terms and define the
probabilistic linguistic utility function
()
()
uLp
when the decision maker is a pessimist as
()
()
()
()
()
0
,
k
t
kk
IL
uLp IL p ϕ
=
=

(8)
where
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28

()
()
() ()
()
() ()
,0
max 2
,,
22
min
,
2
k
kk
k
kk k k
k
kk
k
p
t
IL IL
p
tt
IL p p IL
p
t
IL IL t
p
ϕ

×≤



=× =



×≤


＜
＜
here,
()
k
I
L
is the subscript of the linguistic term
item
k
L
.
Example 2 (continued from Example 1) Suppose
that for the additional insurance
()
1
C
of the
Chinese life insurance company
()
1
A
, the
evaluation information given by the decision makers
can be expressed in a probabilistic linguistic term set
() () ()
{
()
0.15 , 0.2 , 0.1 , 0.3 ,verybad bad medi um good verygood
()
}
0.25
. When the decision maker is an optimist, the
utility function can be calculated by equation (7) as
()
()
0.1 0.3 0.25
120.134
0.2 0.3 0.3
uLp =× + × +× + ×
When the decision maker is a pessimist, the utility
function is given by Equation (8) as
()
()
0.2 0.1 0.1
120.134
0.3 0.3 0.25
uLp =× + × +× + ×
Based on Definition 7 or Definition 8, the utility
function value
()
()
ij ij
uL p
of the evaluation
information
()
ij ij
L
p
of family property insurance
company
i
A
under indicator
j
C
can be
calculated. thus, the combined utility function value
of family property insurance company
i
A
is
defined as
()
()
()
1
1, 2,...,
m
ijijij
j
uA w uL p i n
=
=× =

(9)
In summary, this paper proposes a method for
evaluating family property insurance companies
based on a probabilistic linguistic approximation of
the stochastic dominance criterion in the following
steps.
Step 1: Consumers who have purchased family
property insurance are invited to linguistically
evaluate each evaluation indicator
j
C
of the insurance
company and represent the consumers' evaluation
indicator
j
C
in the form of a probabilistic linguistic
term set.
Step 2: After obtaining the weight evaluation
information in the form of the probabilistic linguistic
term set, it is standardized, and then the weights of
each evaluation indicator are calculated using the
probabilistic linguistic entropy weight method
(shown in Equation (6)).
Step 3: Using Equation (7) or Equation (8), the
linguistic utility function value
()
()
ij ij
uL p
of the
probabilistic linguistic evaluation information given
by the decision maker based on the decision attitude
is calculated, and the utility function matrix is
constructed.
Step 4: Using Equation (9), calculate the
combined linguistic utility function values
()
i
uA
of decision makers regarding the insurance company
i
A
under all indicators
j
C
.
Step 5: Compare the magnitude of the combined
linguistic utility function values between the two
solutions based on almost stochastic dominance
theory, and rank and select the best insurance
company
i
A
based on the obtained combined
linguistic utility function values.
4 EMPIRICAL ANALYSIS
4.1 Evaluation Process
A questionnaire survey was administered to
consumers who had purchased family property
insurance to obtain inWe hope you find the
information in this template useful in the preparation
of your submission.The level of technology and
assets in China has increased dramatically in recent
years, and the number and variety of products
available for people's consumption have been
expanding and enriching. In today's consumer
market, consumer groups are not only concerned
about the quality and reputation of the products
themselves, but also about the personalization of the
products in selecting goods and services. For this
reason, consumers have different attitudes towards
local established companies, small listed companies
and emerging online companies when purchasing
insurance. They choose the right insurance company
for themselves according to their own preferences
and pay more and more attention to the suitability of
insurance companies.
Two representative local established insurance
companies, China Life and Ping An of China, two
small listed companies, Hong Kang Life and
YangGuang Life, and two emerging netflix
companies, Jingdong Financial and
Allianz Financial,
were selected as the insurance companies to be
evaluated, and a questionnaire was designed to
Evaluation of Family Property Insurance Companies based on Probabilistic Linguistic Almost Stochastic Dominance Criterion
29

evaluate the six selected insurance companies based
on the linguistic term set
() () () ()
{
0.15 , 0.2 , 0.1 , 0.3 ,S verybad bad medium good very=
()
}
0. 25good
and the 25 evaluation indexes constructed
in the second part. 150 questionnaires were
distributed, of which 96 valid questionnaires were
returned.
In order to help consumers make better choices
when purchasing family property insurance, this part
uses the proposed probabilistic linguistic almost
random dominance evaluation method to
theoretically analyze the evaluation information and
obtain the ranking of the advantages and
disadvantages of each insurance company to provide
a theoretical basis for consumers to choose a family
property insurance company. Also this part will
demonstrate the operation process of the evaluation
model and verify the feasibility and validity of the
proposed model.
Step 1: Construct the probabilistic linguistic
evaluation matrix based on 96 valid questionnaires
and the definition of probabilistic linguistic term sets.
Step 2: The probabilistic linguistic evaluation
information is standardized, and then each indicator
is assigned a weight using equation (6) to obtain the
weight of each indicator, as shown in Table 4.
Table 4: Factors influencing consumer demand for family
property insurance products.
wei
gh
t
C1 C2 C3 C4 C5 C6 C7
0.05 0.04 0.04 0.05 0.05 0.05 0.03
C8 C9 C10 C11 C12 C13 C14
0.03 0.04 0.04 0.04 0.03 0.04 0.04
C15 C16 C17 C18 C19 C20 C21
0.04 0.04 0.04 0.04 0.04 0.05 0.04
C22 C23 C24 C25
0.04 0.04 0.04 0.03
Step 3: Assuming that the decision maker is an
optimist, the probabilistic linguistic utility function
values
()
()
ij ij
uL p
for the insurance company
i
A
（
1, 2, 6i = 
） under each indicator
j
C
are
calculated using equation (7) and aggregated into a
utility function matrix as follows.
7.7 4.2 2.4 3.3 7.2 7.5 4.6 5.5 3.2 7.6 5.0 5.6
6.2 2.9 6.8 7.2 5.4 4.7 2.6 5.0 6.7 3.1 4.3 6.2
1.5 2.5 3.0 5.7 1.2 1.9 2.8 3.6 5.0 2.8 2.1 2.6
3.2 4.9 8.5 3.4 3.8 3.5 4.0 5.8 6.8 1.7 5.4 5.4
7.5 7.5 7.5 7.0 7.0 4.3 2.0 3.5 0.5 7.0 3.0 2.5
4.4 1.0 5.2 4.0 2.7 7.3
U =
2.3 2.6 3.7 6.0 5.4 0.67










5.6 4.8 5.3 4.8 2.6 3.4 8.3 4.5 5.0 2.2 3.1 6.0 7.9
7.4 4.8 5.5 3.4 6.6 5.6 4.3 4.8 2.4 5.5 4.4 7.6 4.4
5.9 4.1 4.9 2.8 3.5 5.9 3.2 1.6 1.6 3.4 4.8 3.5 0.7
6.8 1.6 2.7 5.8 5.1 2.8 3.7 4.1 4.7 4.4 6.2 2.1 2.5
7.5 7.0 3.5 4.5 4.5 3.5 3.0 7.0 3.0 2.5 3.0 5.5 3.0
2.4 4.3 7.3 3.7 0.3 4.7 3.0 7.3 3.6 5.0 2.0 1.3 2.0










Step 4: Using equation (9), the value of the
combined utility function for each company is
calculated as
() () ()
123
5.068, 5.143, 3.192,uA uA uA===
() () ()
456
4.356, 4.779, 3.8.uA uA uA===
Step 5: Based on the above utility function values,
we get the ranking of each insurance company in
terms of advantages and disadvantages as
215463
A
AAA A A   
.
4.2 Result Analysis
From the above calculation process, it can be seen
that consumers focus on the reasonableness
indicators regarding the setting of family property
insurance products such as the claim settlement,
additional insurance settings, reasonableness of
premiums, and effectiveness of coverage, as well as
the indicators of the degree of credibility ability of
insurance companies when purchasing family
property insurance, while online sales are not the
indicators that consumers focus on when choosing
family property insurance companies for the time
being.
Looking at the primary indicator product
positioning alone, the utility function value of each
insurance company is calculated as
() () () ()
1234
44.43, 47.46, 27.06,uA uA uA uA====
() ()
56
43.95, 46.83, 33.25uA uA==
. In terms of product
design positioning, it can be seen that Ping An of
China has a strong competitive edge, and the product
positioning of Ping An Insurance Company of China
is clear in consumers' minds, which meets people’s
functional needs for the product as well as the
expected loss protection. Looking at the primary
indicator display work alone, the utility function
value of each insurance company are
() () () ( )
1234
23.82, 20.95, 13.4,uA uA uA uA====
() ()
56
19.3, 20, 14.36uA uA==
. At this time, the
service display level of China Life Insurance
Company is higher in consumers’ mind, the
company’s solvency, degree of credibility and other
BDEDM 2022 - The International Conference on Big Data Economy and Digital Management
30

hard strengths are stronger, China Life Insurance
Company’s products have stronger contractual
protection, and the service facade and staff's
reception etiquette are more standardized. Looking at
the primary indicator claims work alone, the utility
function value of each insurance company are
() () () ()
1234
33.59, 34.97, 25.97,uA uA uA uA====
() ()
56
25.81, 33, 30.7uA uA==
. It can be seen that
Ping An Insurance Company of China has a higher
claim settlement rate in consumers’ mind, and
consumers are more inclined to choose Ping An
Insurance Company of China. Looking at the first
level indicator service hours alone, the utility
function values for each insurer are
() ( ) ()
12 3
24.21, 24.19, 14.02,uA uA uA===
() () ()
456
19.91, 17, 13.88uA uA uA===
, It can be
seen that China Life Insurance Company is better
than other insurance companies in terms of empathy
and urgency in the minds of consumers.
Combining these three indicators, Ping An
Insurance Company of China has the strongest
overall strength. Different types of insurance
companies have their own competitive advantages.
Ping An of China and China Life, the two oldest
insurance companies in China's insurance industry,
are stronger than several other major companies in
terms of overall strength, with strong capital and solid
overall strength. Allianz Financial Insurance and
Jingdong Financial Insurance Company, the
emerging Netflix companies, excel in display work
and claims work, focusing on improving the service
quality of family property insurance products while
improving the actual business level of the company
in order to gain consumer recognition. Among the
listed companies, Sun Life and Hong Kang Life were
superior in terms of service timeliness and claims
work. Hongkang Life outperforms other insurance
companies in the underwriting business of family
property insurance, and Sun Life outperforms other
insurance companies in the professionalism of its
surveyors.
Through the above analysis, it is beneficial for
consumers to purchase family property insurance
according to the characteristics and advantages of
each company’s insurance products. In conclusion, if
a family property insurance company wants to get a
long development in the future, besides creating its
own outstanding advantages, it also needs to
“strengthen the weak points” and “fill the short
boards” to better realize the high-quality
development of the company, so as to focus on the
main business, build advantages, win with quality,
standardize the operation, and innovate, and take the
lead in the future. We should focus on our main
business, build up our strengths, win by quality,
standardize our operation, innovate, and take the road
of “specialization and innovation” development.
Now, standing at the new wind of the 14th Five-Year
Plan, companies should grasp the strategic
opportunity period of developing modern insurance
service industry, focus on customers, adhere to high-
quality development, create a healthy structure and
distinctive product system, meet the personalized
needs of consumers in different dimensions, and
devote themselves to building a value insurance
company with differentiated business characteristics
and sustainable development. The company is
committed to building a value-based insurance
company with differentiated business characteristics
and sustainable development capabilities, providing
customers with better quality and reliable products
and services, and continuously promoting product
diversification.
5 CONCLUSIONS
By clarifying the factors that consumers consider
when purchasing family property insurance, this
paper divides the factors that affect consumers’
choice of family property insurance companies into
two aspects, namely, the quality of family property
insurance products and the comprehensive strength of
family property insurance companies, establishes an
index system for evaluating family property
insurance companies from consumers’ perspective,
and proposes a probabilistic linguistic almost random
The probabilistic linguistic almost stochastic method
is proposed for the evaluation of family property
insurance companies. The method first uses the
probabilistic linguistic entropy weighting method to
assign the indexes, which takes into account the
ambiguity and hesitation of the experts in evaluating
the indexes, and improves the accuracy of the index
assignment. Then, the probabilistic linguistic term set
is combined with the almost stochastic dominance
criterion to propose a probabilistic linguistic almost
stochastic dominance decision making method for
calculating the utility value of family property
insurance companies to obtain the strength ranking of
family property insurance companies. The decision
method proposed in this paper fully considers
consumers’ psychological behavioral preferences and
provides a feasible methodological idea for family
property insurance company selection, and the model
can also be extended to the satisfaction evaluation of
Evaluation of Family Property Insurance Companies based on Probabilistic Linguistic Almost Stochastic Dominance Criterion
31

insurance companies with the same type of
characteristics.
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