The Rehabilitation Consumption Decision Analysis of Disabled
Elderly People in Chengdu Based on the Analytic Hierarchy Process
Maoqiang Xu, Asha Hasnimy Mohd Hashim
*
and Zhiwei Chen
Faculty of Education, Universiti Teknologi Malaysia, Malaysia
Keywords: Analytic Hierarchy Process (AHP), Disabled Elderly, Rehabilitation Consumption.
Abstract: The rehabilitation of the disabled elderly is a challenging area in China, as it accounts for a large proportion
of the deeply aging population, and the development of rehabilitation for the elderly is lagging, to analyze the
factors affecting the rehabilitation of the elderly and find the optimal solution. Using Analytic Hierarchy
Process, mathematical statistics and logical analysis, and other related research methods to analyze the 13
factors influencing the consumption demand for rehabilitation consumption of the elderly in Chengdu, the
mathematical model was established by using the arithmetic mean method for judgment matrices of small
order and the eigenvector method for larger ones when performing the weight calculation. There are four main
factors affecting the rehabilitation consumption decisions of the elderly in Chengdu: economic factors,
environmental factors, time factors, and their factors. Among them, the factors that play a decisive role in the
rehabilitation needs of the elderly in Chengdu are: economic factors, environmental factors, and their factors,
and the relevant influence factors constitute the greatest weight. Through the mathematical model
construction, the final calculation simulation i.e. the score of scenario D
1
(consumption) is 0.5841 and the
score of scenario D
2
(no consumption) is 0.4159. Finally, the CR<0.1 for all the single and total sorting
according to the relevant steps shows that the consistency of this judgment matrix is acceptable and logical.
1 INTRODUCTION
Consumption is an important behavior and process of
human socio-economic activities. As China's
economy enters a new normal and the material living
standard of residents continues to improve, residents'
sports culture is also showing vigorous development.
The proportion of residents' sports consumption in
consumption is becoming larger and larger, and
consumption is gradually becoming a new
consumption growth point in China's economy. The
current concept of consumption is gradually gaining
popularity, which has greatly stimulated people's
awareness of consumption (Zhang, 1955). Needs
cannot be substituted for one another (for example, a
lack of water and shelter cannot be offset by more
education or healthcare) They are essential parts of
the same package. And–crucially for the
development of sustainable consumption corridors–
they are intrinsically satiable: there are limits beyond
which more food, more work, or more security are no
*
Corresponding author’s email
longer helpful and could even do one harm. There
comes a point where sufficiency is reached in the
process of meeting needs: this helps constrain the
tendency toward escalating consumption associated
with satisfying consumer wants, threatening to
breach planetary boundaries. The focus on needs and
sufficiency aligns UBS with sustainable
development, aiming to meet current needs without
compromising the ability of future generations to
meet their own need (Coote, 2021). The average
monthly consumption of the surveyed elderly in
Chengdu was 2231.11 RMB, of which 969.39 RMB
was spent on food, accounting for 43.45%c of the
total expenditure, i.e. The Engel coefficient was
0.4345. According to the United Nations Engel
coefficient, the standard of living of the surveyed
older adults is moderate. By the end of 2018, China's
elderly population aged 60 or older reached 249
million, accounting for 17.9% of the total population
(Jiang, 2019). Studies show that more than 95% of
the disabled elderly in countries such as the UK, the
US, and Japan choose to age in place in the
688
Xu, M., Hashim, A. and Chen, Z.
The Rehabilitation Consumption Decision Analysis of Disabled Elderly People in Chengdu Based on the Analytic Hierarchy Process.
DOI: 10.5220/0012042000003620
In Proceedings of the 4th International Conference on Economic Management and Model Engineering (ICEMME 2022), pages 688-693
ISBN: 978-989-758-636-1
Copyright
c
2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
community, and more than 80% in the Philippines,
Vietnam, and Malaysia. The majority of disabled
elderly people in China also want to choose to age at
home or in the community. Therefore, it is important
to identify and meet the long-term care needs of the
elderly with disabilities to promote the construction
of a community-based elderly care service system
and improve the quality of long-term care for the
elderly (Zhang, 1955) with disabilities. The study
found that there were differences in the ability levels
of disabled elderly people by age, gender, education
level, marital status, and residential status. The
(Activities of daily living) ADL is an important
indicator commonly used in academia to measure the
ability of older adults to care for themselves in daily
life and consists of the Somatic Self-Care Scale and
the Instrumental Activities of Daily Living Scale.
interviews, participants were assessed for disability
in 4 key ADL tasks—bathing, dressing, walking, and
transferring (Hardy, 2004). The elderly with
disabilities were classified into three levels according
to the six indicators in the Self-Care of Somatic Life
Scale (eating, dressing, getting in and out of bed by
themselves, going to the toilet, walking around
indoors, and bathing): Mild disability (1~2 items
cannot be completed), moderate disability (3~4 items
cannot be completed) and severe disability (5~6
items cannot be completed) (Liu, 2019). According
to the design of the questionnaire, the 6 indicators of
ADL were replaced by the control of urination and
defecation in the bed. If the respondent answered
"don't need any help" for all 6 items, he/she is fully
self-care; if he/she answered "need help for one
item", he/she is partially self-care; if he/she answered
"need help for two or more items", he/she is unable
to take care of himself/herself.
The main innovations of this paper are as follows:
(1) Rehabilitation of the disabled elderly s lagging
in the current development path in China, and this
paper finds the main factors influencing the
consumption of elderly rehabilitation through
rehabilitation demand analysis.
(2) To investigate the rehabilitation needs of the
elderly with disabilities and to construct a
rehabilitation needs decision model by applying the
hierarchical analysis process.
2 OVERVIEW OF THE
HIERARCHICAL ANALYSIS
CONCEPTION
The Analytic Hierarchy Process (AHP for short) was
proposed by Professor T.L. Saaty, an American
operations researcher, and applied in 1971 in the
study of contingency planning for the U.S.
Department of Defense, as a comprehensive
approach to system evaluation and decision-making
that integrates qualitative and quantitative analysis.
AHP has been widely used in many research areas
such as security, risk assessment, and related decision
problems.
2.1 Basic Characteristics
Complex decision problems are easy by identifying
complex problems as general objectives and then
setting them as minor ones based on several factors
that affect the general objective.
It combines quantitative and qualitative analysis,
expresses human subjective judgment scientifically
in a mathematical way, gives the weight of each
decision option reasonably, finds out the score of
each option, ranks the advantages and disadvantages
of each option, makes the optimal decision, and thus
solves complex practical problems.
2.2 Basic Principle
When studying a complex practical problem, the
problem to be studied is identified as the top goal,
then it is identified as a small goal based on several
factors affecting the total goal, and finally, a
progressive hierarchy is constructed based on the
hierarchical relationship between these related
several small goals, and these small goals are ranked
in order of merit, which is ultimately used as the basis
for problem decision making.
2.3 Calculation Steps
(1) Construct a structural model diagram. Construct a
hierarchical structure based on the indicators
affecting the event, while specifying the relationships
between the hierarchical factors.
(2) Constructing judgment matrix. Based on the
hierarchical model diagram, the relative importance
of the factors at (Zhang, 1955) each level needs to be
judged and presented in a numerical form.
(3) Hierarchical single ranking. The indicators
between the same level are ranked in importance in
terms of the magnitude of their influence on the
previous level.
(4) Overall ranking of levels. Combine the results
of the ranking between each level and calculate the
impact of the weight values on the overall index.
The Rehabilitation Consumption Decision Analysis of Disabled Elderly People in Chengdu Based on the Analytic Hierarchy Process
689
(5) Consistency check. Based on the constructed
judgment matrix, the eigenvectors, and the maximum
eigenvalues are calculated to see if they meet the
specified requirements.
2.4 Hierarchical Analysis Example
Analysis Process, Establishing a
Recursive Hierarchy
The key to determining the success of the Analytic
Hierarchy Process (AHP) is the construction of a
reasonable, comprehensive, and easy-to-judge
recursive hierarchy model. This is also the first step
in applying the hierarchical method. In this paper, the
system is constructed with no more than nine
elements dominated by each element in each level of
the structure. Ultimately, the paper divides these
layers into four categories: purpose layer, criterion
layer, sub-criterion layer, and scheme layer (Zhang,
1955). (Table 1), There are four options for
calculating the weights of the Analytic Hierarchy
Process: geometric mean, arithmetic mean,
eigenvector, and least squares, which are close to
each other in terms of values and usually do not need
to be studied separately in advance but can be
determined in the process of the actual calculation. In
this paper, when performing the calculation of
weights, the arithmetic average method is used for
judgment matrices of small order, and the larger one
uses the eigenvector method.
Table 1: A progressive hierarchy of consumption decisions for rehabilitation of the elderly with mild.
Target layer
A
Guideline layer
B
Sub-criterion layer
C
Program level
Rehabilitation
consumer demand A
Economic FactorsB
1
Retirement pay
C
1
Consumption
D
1
Or no
consumption
D
2
Annual household income
C
2
Rehabilitation Prices
C
3
Environmental Factors
B
2
Distance to the rehabilitation
site
C
4
Rehabilitation Effect
C
5
Rehabilitation service
attitude
C
6
Security Risk Factors
C
7
Time Factor
B
3
Leisure time for the elderly
C
8
Round trip travel time
C
9
Rehabilitation treatment time
C
10
Self-needs
B
4
Assisted Rehabilitation
C
11
Life necessity rehabilitation
C
12
Exercise rehabilitation
C
13
2.4.1 Analysis from the Perspective of
Economic Factors
Literature projections indicate that the total cost of
care for the mildly disabled is currently the highest in
China ($3,040 billion in 2050), followed by the
severely disabled ($1,682 billion in 2050) and the
moderately disabled ($744.9 billion in 2050). Our
mildly disabled elderly have to bear the greatest
financial pressure, which is very testing for their
retirement benefits and their family’s financial
situation. According to the literature, Only 16.74% of
the disabled elderly are entitled to a pension 79.4%
of the disabled elderly in rural areas are supported by
their children, compared to 55% in urban areas.
Therefore, the economic factors considered in this
paper should include retirement salary C
1
and annual
household income C
2
. In addition, the price of
rehabilitation C
3
is the most important factor.
2.4.2 Analysis from the Perspective of
Environmental Factors
This paper identifies distance from the rehabilitation
site, rehabilitation outcomes, service attitudes, and
safety risk factors as the four main factors to consider.
ICEMME 2022 - The International Conference on Economic Management and Model Engineering
690
In terms of the time factor, the elderly’s own leisure
time is the main factor. In addition, it also includes
the travel time to and from the home and the time
spent on rehabilitation treatment. Finally, their own
needs determine whether the elderly are willing to
take rehabilitation treatment. In this paper, we believe
that there are three main categories of mildly disabled
elderly people, namely, assisted rehabilitation,
rehabilitation of life necessities, and rehabilitation of
exercise. The willingness to rehabilitate is different
among these three categories of elderly with mild
disabilities.
2.4.3 Construction of Judgment Matrix
The second step of hierarchical analysis is to
construct the judgment matrix. It is the basis for
measuring the importance of things and the source for
performing weight value calculations. Ask the expert
repeatedly for the criteria of the judgment matrix,
where two elements are compared two by two (with
each other) which is important, and how much and
assign a value to the degree of importance by 1-9
(Table 2).
Table 2: Importance scale of judgment matrix.
Importance Scale Meaning
1 indicates that two elements are of equal importance
compared to each othe
r
1 indicates that two elements are of equal importance
compared to each othe
r
3 indicates that the former is slightly more important
than the latter when compared to the two elements
3 indicates that the former is slightly more important
than the latter when compared to the two elements
5 Indicates that the former is significantly more
important than the latter when compared to the two
elements
5 Indicates that the former is significantly more
important than the latter when compared to the two
elements
7 Indicates that the former is strongly more important
than the latter when com
p
ared to the two elements
7 Indicates that the former is strongly more important
than the latter when com
p
ared to the two elements
9 indicates that the former is more extremely important
than the latter when com
p
ared to the two elements
9 indicates that the former is more extremely important
than the latter when com
p
ared to the two elements
2,4,6,8 denotes the intermediate value of the above judgment
Countdown
If the ratio of the importance of element I to element j
is a
ij
, then the ratio of the importance of element j to
element i is a
ji
=1/a
ij
3
(
no 3
)
The judgment matrix corresponding to each layer (Tab le 3):
Table 3: Judgment matrix corresponding to each layer.
C
1
C
2
C
3
C
4
C
5
C
6
𝐷
𝐷
13
1
3
1
𝐷
𝐷
1
1
3
31
𝐷
𝐷
12
1
2
1
𝐷
𝐷
1
1
5
51
𝐷
𝐷
12
1
2
1
𝐷
𝐷
13
1
3
1
C
7
C
8
C
9
C
10
C
11
C
12
𝐷
𝐷
15
1
5
1
𝐷
𝐷
1
1
3
31
𝐷
𝐷
12
1
2
1
𝐷
𝐷
1
1
2
21
𝐷
𝐷
13
1
3
1
𝐷
𝐷
1
1
5
5
1
C
13
B
1
B
2
B
3
B
4
A
𝐷
𝐷
12
1
2
1
𝐶
𝐶
𝐶
⎣
⎢
⎢
⎢
⎡
1
1
4
1
3
4
1
3
3
1
3
1
⎦
⎥
⎥
⎥
⎤
𝐶
𝐶
𝐶
𝐶
⎣
⎢
⎢
⎢
⎢
⎢
⎡
1
1
2
1
3
1
2
2
1
1
2
1
2
3
2
1
2
2
2
1
2
1
⎦
⎥
⎥
⎥
⎥
⎥
⎤
𝐶
𝐶
𝐶
⎣
⎢
⎢
⎢
⎡
1
1
2
1
3
2
1
1
3
3
3
1
⎦
⎥
⎥
⎥
⎤
𝐶
𝐶
𝐶
⎣
⎢
⎢
⎢
⎡
1
1
2
1
5
2
1
1
2
1
5
2
1
⎦
⎥
⎥
⎥
⎤
𝐵
𝐵
𝐵
𝐵
⎣
⎢
⎢
⎢
⎡
12
1
2
1
1
3
1
3
1
3
2
3
3
1
2
3
1
2
1
2
1
⎦
⎥
⎥
⎥
⎤
In the next step, the: weight values corresponding
to each layer are calculated. As mentioned before, the
simple judgment matrix can be solved directly using
the arithmetic mean method. Firstly, for the sub-
The Rehabilitation Consumption Decision Analysis of Disabled Elderly People in Chengdu Based on the Analytic Hierarchy Process
691
criterion layer, its judgment matrix is simple, and the
weight values of the scheme layer relative to the sub-
criterion layer can be calculated (Table 4).
Table 4: Target layer weight values.
Target
laye
r
B
1
B
2
B
3
B
4
Weight 0.4496 0.2054 0.1052 0.2398
For the target and criterion layers, the matrix
dimensionality is high, and this paper uses the
eigenvector method to determine their weights, as
shown in (Tab le 5), respectively. Take B
1
as an
example, its normalized feature vector: and this
feature vector is used as the weight value.
Table 5: Criterion layer weight values.
Wei
g
hts
B
1
B
2
B
3
B
4
C
1
0.6144 0 0 0
C
2
0.1172 0 0 0
C
3
0.2684 0 0 0
C
4
0 0.4182 0 0
C
5
0 0.2707 0 0
C
6
0 0.1205 0 0
C
7
0 0.1906 0 0
C
8
0 0 0.5278 0
C
9
0 0 0.3325 0
C
10
0 0 0.1396 0
C
11
0 0 0 0.5954
C
12
0 0 0 0.2764
C
13
0 0 0 0.1283
The next step is to consider the weighting
relationships between the layers as a whole. First, the
weights between the criterion and solution layers are
determined. According to (Table 4) target layer
weight values. And, the weight matrix between the
criterion and solution layers is:
𝐷
𝐷
𝐵
0.6690
0.3310
𝐵
0.4994
0.5006
𝐵
0.4002
0.5998
𝐵
0.5781
0.4219
Further, in combination with Table 6, the linkage
between the target and program layers can be
established. Their weights are determined as follows:
0.6690
0.3310
0.4494
0.5998
0.4002
0.5998
0.5781
0.4219
×
0.4496
0.2054
0.1052
0.2398
=
0.5841
0.4159
According to the formula: Among them is the
maximum eigenvalue, which is the matrix order.
Calculate consistency ratio CR=CI/RI, If the value is
less than 0.1, then the consistency of the judgment
matrix is considered to be an acceptable RI Value .
The first is the hierarchical single ranking and
test. The hierarchical single ranking is obtained for
each level. (Table 8). Take the guideline layer B
1
as
an example. Perform consistency checks. The
maximum eigenvalue is Max=3.0735, Consistency
indicators of the judgment matrix: According to
(Figure 5), Find out RI=0.58, Thus the consistency
ratio: Therefore, the guideline level B
1
The
consistency of the judgment matrix is acceptable.
Next, the hierarchical total ranking and test are
performed. The total ranking is shown in Table 3. The
consistency test is performed below.
get
𝐷
= 0.5841
𝐷
= 0.4159
According to the formula： Among them is the
maximum eigenvalue， which is the matrix order.
Calculate the consistency ratio CR=CI/RI, If the
value is less than 0.1, then the consistency of the
judgment matrix is considered to be an acceptable RI
Val ue.
3 CONCLUSION
China has a serious aging problem, and the
prevalence of chronic diseases brought about by
changes in population age structure tends to
aggravate the inherent loss of structural and
functional aging (Thibaut, 2020). Through the above
example analysis process, it can be found that various
factors influence the rehabilitation consumption
decisions made by the disabled elderly in Chengdu.
Mainly includes: 4 major aspects of the economy,
environment, time, and own needs. Meanwhile. The
indicators that evaluate and influence these 4 major
factors, in turn, include: retirement salary, annual
household income, annual household income,
rehabilitation price, rehabilitation location, distance,
rehabilitation effect, attitude toward rehabilitation,
leisure time of the elderly, travel time to and from the
home, rehabilitation treatment time, assisted
rehabilitation, life necessity rehabilitation, and
exercise rehabilitation 13 influence factors. The main
influencing factors listed above are sufficient to
reflect the overall situation affecting the
rehabilitation consumption decisions of the elderly in
Chengdu. Among the environmental factors, the
ICEMME 2022 - The International Conference on Economic Management and Model Engineering
692
rehabilitation distance, rehabilitation effect, service
attitude, safety risk factors, service attitude, and
rehabilitation effect are the most important factors
influencing elderly people's rehabilitation
consumption.
Regarding the "own needs" of rehabilitation
consumption of the elderly in Chengdu, "exercise
rehabilitation", "life necessity rehabilitation" and
"supplementary group rehabilitation" are the main
factors influencing the consumption of rehabilitation
of the elderly in Chengdu. Of the three, "life necessity
rehabilitation" is the most important factor affecting
the rehabilitation of the elderly (Zhou, 2019), That is,
the score of scheme D
1
(consumption) is 0.5841, and
Scenario D
2
(no consumption) scored 0.4159. Finally,
according to the relevant steps to prove that all single
sort and total CR<0.1 for sorting, It means that the
consistency of this judgment matrix is acceptable, it
means that the judgment matrix is logical. In
summary, older adults in Chengdu will choose to
spend money on rehabilitation if their retirement
income is objective, the price of rehabilitation is
appropriate, the rehabilitation effect is good, and they
are satisfied with the service; Conversely, if these
conditions do not meet the expectations of the
disabled elderly in Chengdu, they will influence the
elderly's decision to make rehabilitation
consumption.
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