Research on the Relationship between Architectural Decorative Patterns and their Carriers Based on Analytic Hierarchy Process

Civil Engineering and Urban Planning: An International Journal (CiVEJ ) Vol.7, No.1/2, June 2020
DOI:10.5121/civej.2020.7201 1
RESEARCH ON THE RELATIONSHIP
BETWEEN ARCHITECTURAL DECORATIVE
PATTERNS AND THEIR CARRIERS BASED ON
ANALYTIC HIERARCHY PROCESS
Li Li 1, 2
and Shao Long1
1
School of Architecture, Harbin Institute of Technology; Key Laboratory of Cold
Region Urban and Rural Human Settlement Environment Science and Technology,
Ministry of Industry and Information Technoiogy, China
2
School of Architecture, Inner Mongolia University of Technology, China
ABSTRACT
Architectural decoration is not only a constituent part of architectural style, but also a connotation
expression of the diversity of architectural culture. There is a multi-level relevance between the subject
matter, modeling and implication of architectural decoration pattern and architectural type, space and
units. The related research is an important supplement to the systematic research of traditional
architecture. In view of this, on the basis of detailed investigation and surveying of the research
specimens, analytic hierarchy process (AHP) is applied in this study to divide hierarchy of the decorative
patterns and the architectural identity, compares the weights of the relevance between the hierarchies,
clarifies the complex relationship between the decorative patterns and architecture, and studies the
architectural form and its cultural connotation from the architectural decoration.
KEY WORDS
Carrier of architecture, Decorative pattern, Relevance, AHP
1. INTRODUCTION
Architectural decoration is not only an constituent part of architectural form and style, but also
an expression medium of architectural culture and regional characteristics. It is an important
content of systematic research on traditional architecture and its culture. Nowadays, substantial
amount of traditional architectural decorations are going through rapid destruction and
disappearance due to dereliction and weathering erosion. After renovating, the architectural
decoration forms are also deviating from the historical original to varying degrees. The current
situation does not warrant optimism.
The academic circles have carried out corresponding researches on the field of architectural
decoration and decorative patterns: (1) the researches of the classification and composition, as
well as approaches of decorative patterns in the field of design science [1] [2]. (2) In the field of
architecture, most of the discussions of decorative patterns could be found in the historical data
research, but more of them remain confined in the introductory level, the deeper overall
researches are scarce. Furthermore, there are researches on the aesthetic form of decorative
patterns, guided by pattern theories and composition theories [8] [9]. However, there is no
systematic coverage to the study of the correlation between decorative patterns and carriers. The

2
styles of decorative patterns not only have their own morphological systems, but also show
specific styles in different carriers, which not only enrich the pattern form systems, but also play
important roles in the performance of the carrier forms.
Through long-term research process, it is found that architectural decorative patterns are
characterized by rich architectural carrier types, numerous decorative patterns in carriers,
miscellaneous detailed decorative patterns and various influencing factors, which are also
common problems encountered in the research process of architectural decorative patterns. With
“the research characteristics of specific solutions to specific problems”, the analytic hierarchy
process (AHP) satisfies the research needs of a large number of individual analyses in the study
of architectural decorative patterns. Introducing AHP for analyzing architectural decorative
patterns from a comprehensive and subtle perspective, can fully reflect the logical relationship
between architectural carriers and architectural decorative patterns.
In view of this, the analysis method of AHP is adopted in this research to classify, split and
compare the decorative patterns and building carriers, so as to analyze the multi-level
relationship between the decorative patterns and the carriers in detail.
2. ARCHITECTURAL DECORATION PATTERNS AND CARRIERS
Definition of pattern by Mr. Lei Guiyuan is: “Pattern is a way of conscious creation
performance based on a certain idea to deal with the shape, color, graphics and so on, in order to
cause the aesthetic feeling of the audience” ①
. Based on Mr. Lei Guiyuan’s definition of pattern
and the morphological relationship between pattern and architecture, interpretation of the
architectural decoration pattern in this paper is: Based on the architectural form, the shape,
color, graphics and other elements are processed to form a pattern form that is consistent with
the architectural form, and at the same time, which would help to express the connotation of
architectural culture.
Through extensive field research by the research group of traditional architecture and decorative
patterns, it has been learned that: architectural decoration pattern not only covers the three basic
elements constitute patterns: shape, pattern, color②
, but also subject to the constraints of the
carrier, and there is a close relevance with the carrier. According to their form, the approaches
of different building units displaying their decorative patterns vary from each other; even the
same type of buildings display different styles of decorative patterns due to the different
construction years; the same decorative pattern on different scales of the same kind of building
units present in different forms; with different types of carriers, the form of patterns differentiate
from each other; different types of architecture adopt different patterns. These kinds of
phenomenon all reflect a rich relationship between architectural decoration patterns and
architectures. Religious architectural decoration patterns are mostly to preach doctrine as the
main idea; Residential architectural decoration patterns are mostly reflecting the people’s
aspirations of the construction age; official architectural decoration patterns reflect the supreme
right of those in power.
3. ANALYSIS METHOD
3.1. Analytic Hierarchy Process
The analytic hierarchy process (AHP) originated from T. L. Saaty, a famous American
operations researcher and professor of the University of Pittsburgh. In the 17th century, with the
emergence of enormous data, it became a problem that factors cannot be expressed

3
quantitatively, which brought great inconvenience to decision-makers. analytic hierarchy
process was meant to solve this problem. In China, AHP has extensive; it has been widely used
in economy, policy making, management, project planning, engineering and other fields.
Analytic hierarchy process has the characteristics of strong practicability, flexibility and
operability, which can simplify the complex and large amount of complex problems. ③
In the
study of the relevance between architectural decoration patterns and architectural carriers, the
biggest challenge is the large amount of data, the miscellaneous types of architectural decoration
patterns, and the various types of traditional building units, which increase the difficulty of the
research on their relevance. By using the analytic hierarchy process, through the split and
quantitative analysis of the “targeted factors”, the research goals are matched one on one
correspondingly, and the relationship between the architectural carriers and the decorative
patterns reflected in the current status of architectural decoration as well as the application rules
are clarified.
3.2. Process Analysis
The application of analytic hierarchy process to analyze the research object, first of all, the
different factors of each problem are broken down into: target layer, guideline layer and scheme
layer. Through the weight comparison between the hierarchies to conduct analysis and
comparison. Using analytic hierarchy process to study the relevance between the architectural
decoration pattern and its carrier, the relevance can be set as the overall goal, the architectural
carrier unit is set as the guideline layer, the decoration pattern is set as the scheme layer, and the
weight calculation is calculated according to the upper and lower containment relationship
between the elements. The analysis process includes: 1. Establishing the scale hierarchy of the
problem; 2. Constructing one on one judgment matrix; 3. Calculating the relative weight of the
elements being compared by the judgment matrix; 4. Calculating the combined weight of the
elements of each layer; and 5. Performing the consistency test [5]
.
Through the establishing of hierarchical structure, the index evaluation of architectural unit
hierarchy and decorative pattern hierarchy is carried out, and comparison of weight for
evaluation indexes of different hierarchies is made. The weight was reflected by the scaling of
“1-4” (1: not important, 2: important, 3: very important, 4: extremly important), and the matrix
of one on one weight comparison was formed. Calculating the weight of architectural unit
hierarchy and decorative pattern hierarchy index (Wi), as well as the factor quantity order (n) of
architectural unit hierarchy and decorative pattern hierarchy, and judge the maximum eigen
value of matrix X. The calculation formula is as the following (1):
𝜔𝑖 = (∏ 𝑋𝑖𝑗
𝑚
𝑗=1
)1/𝑛
/ ∑(∏ 𝑋𝑖𝑗
𝑛
𝑗=1
)1/𝑛
𝑛
𝑖=1
𝜆𝑚𝑎𝑥 = ∑(Xω)𝑖/𝑛
𝑛
𝑖=0
𝜔𝑖
(1)
Through geometric averaging and normalization processing of the characteristic vectors of each
row of the judgment matrix, to obtain the weight vector w corresponding to the architectural
unit element and the decorative pattern element:
ω=（ω1,ω2,ω3,ω4,…ωn）
Compare the results for consistency to obtain the consistency index CI. Use the consistency
index and the random consistency index RI to calculate the consistency ratio CR. The formula is
(2):

4
CI = (𝜆𝑚𝑎𝑥 − n)/(n − 1)
CR = CI/RI (2)
When consistency test result CR is smaller than 0.1, it passes the consistency test. In addition,
when the values of n in the formula are equal to 1, 2, 3… 9, the random consistency index
values are 0, 0.52, 0.89, 1.12, 1.24, 1.32, 1.44 and 1.45respectively.
When the calculation results pass the consistency test, it is proved that the weight values of the
above-mentioned indexes at all levels are established, and the factors with high weight values
are of higher importance to the research subject. On the contrary, the importance is low. In this
approach, the relevance and degree of relevance between the architecture carriers and the
decorative patterns are obtained.
4. APPLICATION OF RELEVANCE RESEARCH BASED ON ANALYTIC
HIERARCHY PROCESS: A CASE STUDY OF THE LONGSHENG ZHUANG
RESIDENTIAL AREA
4.1. Overview of Longsheng Zhuang
Longsheng Zhuang is located in Fengzhen City, southeast of Ulaanchab City, Inner Mongolia,
China. It is one of the earliest market towns in Ulaanchab area. In the year Qianlong 12 (AD
1747), the recruited landless farmers from Shanxi, Hebei and Shaanxi were settled here [12],
[13]
.Longsheng Zhuang traditional village is a rare traditional village in existence with a
relatively large scale and a more complete system in Inner Mongolia. Its residential buildings
are large in number, rich in variety and with exquisite decoration (figure 1). Longsheng Zhuang
was named as the first batch of National traditional villages in 2012 and the sixth batch of
famous Chinese historical and cultural towns in 2014. The traditional residential buildings in
Longsheng Zhuang area are rich in decorative patterns and well preserved (Table 1). Taking the
traditional residential buildings in Longsheng Zhuang area as an example, AHP is adopted in
this research to study the relevance between the architectural decoration patterns and
architectural carriers of traditional residential buildings in Longsheng Zhuang district.
Table 1. Status of Longsheng village dwelling house
decoration
Buildingunit Gablefront
Lintel
Doorpanel Rooftopetc.
Status of
architectural
decoration
Fig.1The full view of Long shengzhuang

5
4.2. Analysis of the Relevance Between Architectural Decoration Patterns and
Carriers
Based on extensive on-the-spot investigations on the traditional residential buildings in
Longsheng Zhuang, combined with the decomposition of the relevant characteristics of the
decorative patterns, this research sort outs the characteristics of the relevance between the
architectural decorative patterns and the units from the aspects of the architectural units and the
architectural decorative patterns, and set it as the basis for the selection of indexes, and revises
the index system by taking into account of the opinions of the local residents and relevant
scholars to establish an relevance characteristics evaluation index system of the architectural
decoration patterns and building units in accordance with the actual situation of Longsheng
Zhuang residential complex.
The indexes in the basic characteristic evaluation index system is graded on the relevance
scaling of 1 to 4, and one on one comparison are given to determine the close degree of
relevance between the factors, and the weight of the indexes at all levels is
calculated（Table1.2）.
Table 2. Primary evaluation index questionnaire for the relevance between architectural decorative
patterns and carriers in Longsheng Zhuang residential complex
Evaluation index Characterization Relevance
Gable front Most of them are located on both sides of the house with hard Gables to
support the front and back eaves
1 2 3 4
Lintel Upper part of door frame, lintel 1 2 3 4
Door panel Main decorative component of the door 1 2 3 4
Rooftop etc Roof, ableboard, etc. 1 2 3 4
Table 3. Secondary evaluation index questionnaire for the relevance between architectural
decorative patterns and carriers in Longsheng Zhuang residential complex
The target layer
Primary
index (B)
Secondary index (C)
Characterization of
Secondary index
Relevance of
secondary index to
primary index
Influence factor of
relevance between
architectural decorative
pattern and carrier in
Longsheng Zhuang
residential complex (A)
Gable front
(B1)
Geometrical pattern
(c11)
Line, circle, square,
triangle, etc.
1 2 3 4
Pattern of plants
(c12)
Rolling grass, water lily,
lotus, etc.
1 2 3 4
Pattern of animals
(c13)
Tigers, lions, bats, etc.
1 2 3 4
Lintel (B2)
Geometrical pattern
(c21)
triangle, etc.
1 2 3 4
Pattern of plants
(c22)
lotus, etc.
1 2 3 4
Pattern of animals
(c23)
1 2 3 4
Door panel
(B3)
Geometrical pattern
(c31)
triangle, etc.
1 2 3 4
Pattern of plants
(c32)
lotus, etc.
1 2 3 4
Pattern of animals
(c33)
1 2 3 4
Rooftop and
so on (B4)
Geometrical pattern
(c41)
triangle, etc.
1 2 3 4
Pattern of plants
(c42)
lotus, etc.
1 2 3 4
Pattern of animals
(c43)
1 2 3 4

6
According to the actual condition of the residential complex in Longsheng Zhuang, 4 primary
indexes and 12 secondary indexes (with 3 as a group) were obtained. After all levels of indexes
are weighted for statistics, the evaluation table is obtained, and the consistency test is
performed(Table4.5).
According to the above weight calculation value (WI), it can be seen that: among the traditional
residential buildings in Longsheng Zhuang area, the most common decorative pattern types on
gable fronts (B1) are plant patterns (C12), the most common decorative pattern types on lintels
(B2) are plant patterns (C22), the most common decorative patterns on door panel (B3) are
geometric patterns (C31), and the most common decorative patterns on rooftops and other
structures (B4) are animal patterns (C43). The data obtained by using the analytic hierarchy
process are highly agree with the actual situation on the spot, which also proves the decorative
characteristics that the architectural decorations of residential buildings are most commonly
found on the gable fronts, rooftops as well as doors and windows components, and subject
matter of the decorative pattern is mainly plant patterns and geometric patterns. At the same
time, the feasibility of AHP in this field is verified by result analysis of the case study.
Table 4. Scoring table of the primary index data
Primary
indexes
Data values
B1 B2 B3 B4 Wi
B1 1 3.2451 2.4525 3.9653 0.493186137
B2 0.3081 1 0.7634 1.896 0.170048644
B3 0.4077 1.3099 1 3.6477 0.245836893
B4 0.2521 0.5274 0.2741 1 0.090928327
λmax 4.06308512
CR 0.023627386
Table 5. Scoring table of secondary index data
Prim
ary
inde
xes
Seco
ndary
index
es
Data values Pri
mar
y
inde
xes
Seco
ndar
y
inde
xes
Data values
C11 C12 C13 Wi C21 C22 C23 Wi
B1 C11 1 0.645
3
3.355
1
0.385
5
B2 C21 1 1.2546 2.0546 0.4355
C12 1.549
6
1 3.431
4
0.452
6
C22 0.797
0
1 0.7541 0.2797
C13 0.298
0
0.291
4
1 0.161
8
C23 0.486
7
1.3260 1 0.2847
λmax 3.079254602 3.068284404
CR 0.076206348 0.065658081
C31 C32 C33 Wi C41 C42 C43 Wi
B3 C31 1 2.756
2
2.467
3
0.543
3
B4 C41 1 0.4187 0.3762 0.1761
C32 0.361
6
1 2.014
6
0.264
7
C42 2.388
3
1 0.7891 0.3820
C33 0.405
3
0.496
3
1 0.191
8
C43 2.658
1
1 0.4417
λmax 3.084537638 3.007002253
CR 0.081286191 0.006732935

7
In addition, by analyzing the comparison data of the weights of all layers of the building units
and the decorative patterns, we can obtain that: 1. The frequency of using the same decorative
pattern in different units of the same building; 2. The frequency of using the same decorative
pattern in the same unit of different buildings; 3. The expression of the same pattern element in
different architectural decorative pattern forms and the hierarchical relationship with the
architectural carriers (Table 6). Take gable fronts as the example: According to the research
data, it can be found that the most commonly used decorative patterns of gable fronts in
Longsheng Zhuang houses are plant patterns (with a weight ratio of 0.4526), followed by
geometric patterns (with a weight ratio of 0.3855), and that of the lowest frequency are animal
patterns (with a weight ratio of merely 0.1618), which reflects the influence of architecture
types and units on the use of decorative patterns. Due to the limitation of the class, the
decorative patterns of the residential buildings are mainly plants (Figure 2), and even if the
decorative elements are the same in the decoration of gable fronts, the decorative styles and
expressions of hierarchy relationship of different residential houses are different. Through the
analysis of the relevance between the decoration pattern and architecture of the traditional
residential buildings in Longsheng Zhuang, the correspondence between the two is clarified to a
great extent, which is of practical guiding significance to the renovation and maintenance in a
later stage for the Longsheng Zhuang architectural complex.
Fig. 2 The form of plant patterns in Gable fronts
5. CONCLUSIONS
In architectural integrity studies, the research of architectural decoration patterns can enrich the
research content from the subtle point of view. By analyzing the relevance between architectural
decoration patterns and architectural carriers, we can clarify the application characteristics of
decoration patterns in different architectural types and units. In this research, AHP is adopted to
obtain the ratio relationship of relevance between decorative patterns and architectural carriers
through the analysis process of deconstruction of the hierarchies, construction of matrix and
comparison of weight. Taking the decorations of traditional residential buildings in Longsheng
Zhuang area as an example, in this research, the relevance between the architectural decoration
patterns and the carriers of traditional residential buildings is specifically analyzed. The analysis
results revealed that the research results of the relevance between the architectural decoration
patterns and carriers by applying AHP are consistent with the existing situation, which
demonstrates that this method is suitable for this kind of research. The introduction of analytic
hierarchy process will provide new ideas and approaches for the research of decorative pattern
Table 6. Relationship between decorative pattern
and architecture
Application of sunflower decoration in different units in the
same architecture
Wall surface Gable front Details of Sunflower
decoration
Application of the same unit decoration in different
architectures
Overall view Detail view

8
field, which would have important reference values for the follow-up research of decorative
patterns in other types of carriers. The specific numerical results of the study would also provide
scientific data and theoretical basis for subsequent decoration development of different types of
architecture.
The Figures and Tables in the Research are all Self-Photographed and
Self-Drawn by the Author.
Annotation:
1 Lei Kuiyuan: New patterns [M]. Shanghai: National Compilation and Translation House, January
1949. Page 13.
2 Lei Kuiyuan: New patterns [M]. Shanghai: National Compilation and Translation House, January
1949. Page 13.
3 Xu Shubo: A Practical Decision-making Method: Analytic Hierarchy Process [M], Tianjin: Tianjin
University Press, May 1988. Page 1
REFERENCES
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[12] Liang Jizu. Legendaries of Longsheng Zhuang [M]. Edited by the Research Institute of Culture and
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[13] Compilation Committee of Fengzhen City. Chronicles of Fengzhen City [Z]. Hohhot: Inner
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Funded Projects: National Natural Science Foundation of China (Item Number: 51808299)
AUTHORS
LILI, 1980, Doctor, School of Architecture, Harbin Institute, Research direction:
cultural lands cap.

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