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Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10121
www.etasr.com Nguyen: The Improved CURLI Method for Multi-Criteria Decision Making
The Improved CURLI Method for Multi-
Criteria Decision Making
Anh-Tu Nguyen
Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam
tuna@haui.edu.vn
(corresponding author)
Received: 5 December 2022 | Revised: 26 December 2022 | Accepted: 31 December 2022
ABSTRACT
Multi-Criteria Decision Making (MCDM) investigates the best available choice in the presence of multiple
conflicting criteria, whereas the Collaborative Unbiased Rank List Integration (CURLI) method has been
proposed recently and has been applied in various fields of daily life. However, most previous works
concentrated on analyzing cases in which the factor of a criterion is a specific quantity. The present paper
proposes an approach developed from the original CURLI method, named Improved CURLI. This
improvement helps solve a problem when the factors of the criteria can be linguistic variables or a data set.
The proposed method is applied to rank the alternatives for two case studies: choosing the best grinding
wheel and the best service suppliers. The ranking results are compared to those obtained using other
methods. Furthermore, sensitivity analysis is also conducted to examine the stability and reliability of the
ranking results in various scenarios. The results demonstrate the validity of the Improved CURLI method
and prove that it is applicable for making decisions in various fields.
Keywords-MCDM; CURLI method; improved CURLI method; data set
I. INTRODUCTION
The concept of MCDM is increasingly being used in
various fields [1, 2]. MCDM problems are mentioned as
MCDA or MADM. The essence of MCDM is evaluating and
ranking the available options in order to select the best and
avoid the worst. Researchers have suggested different MCDM
approaches, and many of them have been applied in a variety
of contexts [1, 3]. However, the original versions of the
MCDM approaches are deemed inadequate for circumstances
in which the criteria are expressed as a set of factors or
linguistic variables [4, 5]. The main reason for this
phenomenon is that the uncertainty about the object depends on
a lot of factors, like experts’ opinions, time, location, the way
of data collection, etc. [6]. To deal with this issue, approaches
that combine the fuzzy method with MCDM have been
proposed. That combination is referred to as fuzzy - MCDM.
Many studies are progressively employing the fuzzy - MCDM
methods. For instance, TOPSIS integrated with fuzzy is used in
many applications such as supplier selection [7], project
selection [8], healthcare software [9], supply chain
management [10], manager selection [11], etc. In [12], a fuzzy
VIKOR – MDCM is proposed to analyze and evaluate the
quality of information security policies as well as the content of
press agencies in Gulf countries. Realizing this method’s
exploitation potential, numerous investigations have been
launched in different tasks like warehouse location selection
[13], mobile services [14], and sustainable development in
Islamic countries [15]. In other approaches, the fuzzy
MARCOS method is utilized for road traffic risk analysis [16],
assessment of drone-based city logistics [17], e-service quality
in airline industry [18], and so on.
When applying fuzzy MCDM, it is necessary to determine
the weights of the criteria which play an important role to make
the final decision [19-21]. In this manner, calculating the
weights for the criteria is relatively complex, time-consuming,
and difficult in situations requiring prompt decision-making.
Furthermore, the ambiguity of the decision makers (or
surveyed experts) regarding the research object influences the
weights determined by these methods. Hence, the accuracy of
the weights after the calculation is not guaranteed. As a result,
no longer will the ranking of the options be certain [22-24]. In
addition, most fuzzy MCDM methods still inherit some stages
from the original MCDM methods, one of which is data
normalization. But the data normalization processes of the
MCDM methods are also not the same, leading to the ranking
results of the alternatives also being highly dependent on the
data normalization and sensitive to change [25-27].
Generally, despite the widespread application of fuzzy
MCDM approaches, they still have limitations to some extent.
If a suggested MCDM method can solve two major problems,
it will make significant contributions to this field. Due to the
mentioned limitations associated with the right determination
for the criteria and the normalization of data, it is necessary to
propose an MCDM approach that does not require the
determination of weights for the criteria and the metric
normalization. To overcome these issues, the CURLI method
was first introduced in 2016. It is used to rank applicants for
medical programs [28]. Despite the fact that it has existed for
Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10122
www.etasr.com Nguyen: The Improved CURLI Method for Multi-Criteria Decision Making
six years, only a handful of research projects about this
technique have been carried out. The applying CURLI method
is proposed to inspect the quality of the X12 steel grinding
process [29]. A turning test progress based on the CURLI
approach was designed in [30]. The result reveals that the
proposed method is as precise as the PEG method and better
than the PSI method. In addition, recent works have shown that
the CURLI method is just as accurate as the R and CODAS
approaches to ranking robots, just as accurate as the R, SAW,
WASPAS, TOPSIS, VIKOR, MOORA, COPRAS, and PIV
approach to rating the turning process, and just as accurate as
the R and MABAC approaches to ranking bridge construction
[31]. However, all the above mentioned studies are only
considered when the criteria are clearly defined (not fuzzy set).
In this paper, an approach based on the original CURLI
method, which allows overcoming the mentioned drawbacks is
proposed. The key contributions of the current paper are:
This paper proposes an improved CURLI method to allow
solving the MCDM problems, when the factors of the
criteria can be linguistic variables or a data set.
The proposed method does not need the input data to be
normalized or the weights of the criteria to be evaluated.
The proposed approach is the first step towards enhancing
the CURLI method to optimize MDCM problems as well as
applying it to various fields of daily life.
II. THE IMPROVED CURLI METHOD
The original CURLI method involves four steps as follows
[28-31]:
Step 1: Establish a decision-making matrix with m options
and n criteria as in Table I. Cij is the factor of criterion j
th
in
option i
th
, where i = 1 ÷ m, j = 1 ÷ n.
TABLE I. DECISION-SCORE MATRIX
Alternatives
Criteria
C1 C2 Cj Cn
A1 C11 C12 C1j C1n
A2 C21 C22 C2j C2n
Ai Ci1 Ci2 Cij Cin
Am Cm1 Cm2 Cmj Cmn
Step 2: Create score-point matrices of level m. In criterion
j, the entry corresponding to row t and column v (1 t, v m)
is determined based on the following regulations:
If the factor of criterion j in alternative At is worse than that
of alternative Av, the entry in the corresponding row and
column will be scored as -1.
If the factor of criterion j in alternative At is better than that
of alternative Av, the entry in the corresponding row and
column will be scored as 1.
If the factor of criterion j in alternative At is equal to that of
alternative Av, the entry in the corresponding row and
column will be scored as 0.
All the entries on the main diagonal will be blank. After
this step, n square score-point matrices are established in total.
Step 3: Create the process score-point matrix. The entries
of this matrix are calculated by summing all the corresponding
entries of the score-point matrix in step 2.
Step 4: Rearrange the process score-point matrix. The
arrangement will be performed by moving the rows and
columns of the process score-point matrices by the following
rules: the order of columns from the left to the right
corresponding to the order of the rows from the top to the
bottom. The number of the negative and zero entries above the
main diagonal is maximal. After sorting, the solution in the first
row will be the best choice. Priority of selection reduces from
the first to the last row.
The CURLI approach has been used extensively to solve
optimization problems in several disciplines, in which the
factors of each criterion at an alternative are a specific quantity.
However, in reality, a criterion may be represented by
linguistic variables or a data set. This paper proposes an
approach based on the original CURLI method for handling
these issues as follows:
Step 1: Establish a decision-making matrix as in Table II.
Step 2: Create score-point matrices. This step is
implemented similarly to the original CURLI. However, the
score-point matrices will be determined with every factor of the
criteria. The score point of each criterion is denoted as pf
(1 f k), where k is the number of factors of a criterion.
TABLE II. DECISION-MAKING MATRIX WITH MULTI-
CHOICE OF CRITERIA IN EACH SOLUTION
Alternatives
Criteria
C1 C2 Cj Cn
A1
(C
1
11, C
2
11,…,
C
k
11)
(C
1
12, C
2
12,…,
C
k
12)
(C
1
1j, C
2
1j,…,
C
k
1j)
(C
1
1n, C
2
1n,…,
C
k
1n)
A2
(C
1
21, C
2
21,…,
C
k
21)
(C
1
22, C
2
22,…,
C
k
22)
(C
1
2j, C
2
2j,…,
C
k
2j)
(C
1
2n, C
2
2n,…,
C
k
2n)
Ai
(C
1
i1, C
2
i1,…,
C
k
i1)
(C
1
i2, C
2
i2,…,
C
k
i2)
(C
1
ij, C
2
ij,…,
C
k
ij)
(C
1
in, C
2
in,…,
C
k
in)
Am
(C
1
m1, C
2
m1,…,
C
k
m1)
(C
1
m2, C
2
m2,…,
C
k
m2)
(C
1
mj, C
2
mj,…,
C
k
mj)
(C
1
mn, C
2
mn,…,
C
k
mn)
Step 3: Build the process score-point matrix. The entries of
this matrix are calculated based on the sum of all points in
corresponding marking point matrices. The detailed
formulation is expressed as:
1
k
f
j
j
p
p
k
(1)
Step 4: Rearrange the process score-point matrix. This step
is the same as in the original CURLI method.
III. VERIFICATION STUDY AND DISCUSSION
A. Case Study 1
In this sub-section, the proposed method is applied to
determine which grinding wheel to choose in an MCDM
problem [32, 33]. There are 8 different types of grinding
wheels (A1 ÷ A8), and each wheel is described by 7 criteria
(C1 ÷ C7). Each criterion has 3 alternatives. The decision is
Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10123
www.etasr.com Nguyen: The Improved CURLI Method for Multi-Criteria Decision Making
made to satisfy the conditions: (a) for C7 the smallest is the
best and (b) for the other criteria, the biggest is the best. The
objective of MCDM is to identify the alternative that
simultaneously assures that C7 is the smallest and the
remaining criteria (from C1 to C6) are maximal. This work has
also been accomplished by employing the Fuzzy TOPSIS
method [33] and 6 variations of the VIKOR method [32]. The
results of rating the alternatives using these two ways will be
compared to the results of ranking the alternatives using the
proposed method in this study.
In the first step, the decision-making matrix is composed as
in Table III. In the second step, scoring for the criteria will be
performed. In this case, the value of each criterion at each
alternative has three levels of values. The number of
alternatives that need to be ranked is 8. Thus, the score for each
alternative (for each criterion) is a set of numbers as shown in
(2):
1 2 3P P , P , P with 1 8fj j j j j j N (2)
After the scoring process, the decision-score matrixes are
illustrated from Table IV to Table X. In the next step, the
process score-point matrix is determined based on (1) and is
presented in Table XI. The process score-point matrix is
rearranged based on the mentioned rules in Section 2.
Following the arranging procedure, the alternative in the first
row could be seen as the best choice. The final arrangement is
shown in Table XII.
TABLE III. DECISION-SCORE MATRIX FOR CHOOSING A GRINDING WHEEL [32, 33]
Alternatives
Criteria
C1 C2 C3 C4 C5 C6 C7
A1 (2700, 3200, 3700) (391, 451, 511) (2925, 3475, 4025) (581, 756, 931) (12, 17, 22) (2.65, 4.15, 5.65) (12, 18, 24)
A2 (2000, 2400, 2800) (590, 690, 790) (4275, 4975, 5675) (1099, 1324, 1549) (68, 98, 128) (2.2, 3, 3.8) (45, 60, 75)
A3 (4400, 5000, 5600) (725, 850, 975) (6000, 6900, 7800) (1282, 1532, 1782) (9, 13, 17) (3.55, 4.5, 5.45) (714, 864, 1014)
A4 (2600, 3000, 3400) (350, 400, 450) (3200, 3800, 4400) (729, 879, 1029) (21, 30, 39) (3.15, 4, 4.85) (107, 152, 197)
A5 (7300, 8000, 8700) (818, 953, 1088) (5900, 6700, 7500) (4188, 4688, 5188) (950, 1200, 1450) (6.45, 8.6, 10.8) (1050, 1300, 1550)
A6 (2150, 2550, 2950) (370, 440, 510) (3950, 4600, 5250) (400, 480, 560) (150, 200, 250) (2.6, 3.1, 3.6) (6.5, 10, 13.5)
A7 (2400, 2800, 3200) (385, 460, 535) (1421, 1721, 2021) (425, 600, 775) (55, 90, 125) (1.95, 2.5, 3.05) (36, 50, 64)
A8 (900, 1200, 1500) (115, 160, 205) (1350, 1750, 2150) (495, 620, 745) (1.4, 2.2, 3) (5.75, 8.2, 10.7) (33, 45, 57)
TABLE IV. SCORE-POINT MATRIX FOR CRITERION C1
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
-1, -1, -1 1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A2 1, 1, 1
1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
A3 -1, -1, -1 -1, -1, -1
-1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A4 1, 1, 1 -1, -1, -1 1, 1, 1
1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A5 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 1, 1, 1 -1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1
1, 1, 1 -1, -1, -1
A7 1, 1, 1 -1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
-1, -1, -1
A8 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
TABLE V. SCORE-POINT MATRIX FOR CRITERION C2
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
1, 1, 1 1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, 1, 1 -1, -1, -1
A2 -1, -1, -1
1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A3 -1, -1, -1 -1, -1, -1
-1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A4 1, 1, 1 1, 1, 1 1, 1, 1
1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
A5 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1 1, 1, 1
1, 1, 1 -1, -1, -1
A7 1, -1,-1 1, 1, 1 1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1
-1, -1, -1
A8 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
TABLE VI. SCORE-POINT MATRIX FOR CRITERION C3
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1 -1, -1, -1
A2 -1, -1, -1
1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A3 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A4 -1, -1, -1 1, 1, 1 1, 1, 1
1, 1, 1 1, 1, 1 -1, -1, -1 -1, -1, -1
A5 -1, -1, -1 -1, -1, -1 1, 1, 1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 -1, -1, -1 1, 1, 1 1, 1, 1 -1, -1, -1 1, 1, 1
-1, -1, -1 -1, -1, -1
A7 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
-1, 1, 1
A8 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, -1, -1
Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10124
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TABLE VII. SCORE-POINT MATRIX FOR CRITERION C4
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A2 -1, -1, -1
1, 1, 1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A3 -1, -1, -1 -1, -1, -1
-1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A4 -1, -1, -1 1, 1, 1 1, 1, 1
1, 1, 1 -1, -1, -1 -1, -1, -1 -1, -1, -1
A5 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
1, 1, 1 1, 1, 1
A7 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
1, 1, -1
A8 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1 -1, -1, 1
TABLE VIII. SCORE-POINT MATRIX FOR CRITERION C5
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
1, 1, 1 -1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
A2 -1, -1, -1
-1, -1, -1 -1, -1, -1 1, 1, 1 1, 1, 1 -1, -1, -1 -1, -1, -1
A3 1, 1, 1 1, 1, 1
1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
A4 -1, -1, -1 1, 1, 1 -1, -1, -1
1, 1, 1 1, 1, 1 1, 1, 1 -1, -1, -1
A5 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1 1, 1, 1
-1, -1, -1 -1, -1, -1
A7 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 1, 1, 1 1, 1, 1
-1, -1, -1
A8 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
TABLE IX. SCORE-POINT MATRIX FOR CRITERION C6
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
-1, -1, -1 1, 1, -1 1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 1, 1, 1
A2 1, 1,
1, 1, 1 1, 1, 1 1, 1, 1 1, 1, -1 -1, -1, -1 1, 1, 1
A3 -1, -1 , 1 -1, -1, -1
-1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1 1, 1, 1
A4 -1, 1, 1 -1, -1, -1 1, 1, 1
1, 1, 1 -1, -1, -1 -1, -1, -1 1, 1, 1
A5 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1 -1, -1, -1
A6 1, 1, 1 -1, -1, 1 1, 1, 1 1, 1, 1 1, 1, 1
-1, -1, -1 1, 1, 1
A7 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
1, 1, 1
A8 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1
TABLE X. SCORE-POINT MATRIX FOR CRITERION C7
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
-1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1 1, 1, 1 -1, -1, -1 -1, -1, -1
A2 1, 1, 1
-1, -1, -1 -1, -1, -1 -1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1
A3 1, 1, 1 1, 1, 1
1, 1, 1 -1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1
A4 1, 1, 1 1, 1, 1 -1, -1, -1
-1, -1, -1 1, 1, 1 1, 1, 1 1, 1, 1
A5 1, 1, 1 1, 1, 1 1, 1, 1 1, 1, 1
1, 1, 1 1, 1, 1 1, 1, 1
A6 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1 -1, -1, -1
-1, -1, -1 -1, -1, -1
A7 1, 1, 1 -1, -1, -1 -1 -1, -1, -1 -1, -1, -1 1, 1, 1
1, 1, 1
A8 1, 1, 1 -1, -1, -1 -1 -1, -1, -1 -1, -1, -1 1, 1, 1 -1, -1, -1
TABLE XI. SCORE-POINT MATRIX FOR THE EVALUATION PROCESS
Alternatives
Points
P1 P2 P3 P4 P5 P6 P7 P8
A1
1 2.3333 -0.333 5 -1 -3.6667 -5
A2 -1
3 -3 5 0.3333 -3 -3
A3 -2.3333 -3
-3 3 -3 -3 -3
A4 0.3333 3 3
5 1 -1 -3
A5 -5 -5 -3 -5
-5 -5 -5
A6 1 -0.3333 3 -1 5
-1 -3
A7 3.6667 3 3 1 5 1
-0.3333
A8 5 3 3 3 5 3 0.3333
Table XII indicates that all the entries above the principal
diagonal are negative, therefore A5 is the best choice and A8 is
the worst one. The rank of alternatives is as follows: A5 > A3 >
A6 > A2 > A1 > A4 > A7 > A8. In Table XIII, the ranking
results of the present study are compared to Fuzzy TOPSIS
method [33] and 6 variants of the VIKOR method.
Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10125
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TABLE XII. THE PROCESS SCORE-POINT MATRIX AFTER REARRANGEMENT
Alternatives
Points
P5 P3 P6 P2 P1 P4 P7 P8
A5
-3 -5 -5 -5 -5 -5 -5
A3 3
-3 -3 -2.3333 -3 -3 -3
A6 5 3
-0.3333 -1 -1 -1 -3
A2 5 3 0.3333
-1 -3 -3 -3
A1 5 2.3333 1 1
-0.3333 -3.6667 -5
A4 5 3 1 3 0.3333
-1 -3
A7 5 3 1 3 3.6667 1
-0.3333
A8 5 3 3 3 5 3 0.3333
TABLE XIII. THE COMPARISON AMONG DIFFERENT METHODS FOR CHOOSING THE GRINDING WHEEL
Alternatives
Methods
Original
VIKOR
Comprehensive
VIKOR
Fuzzy
VIKOR
Regret
VIKOR
Modified
VIKOR
Interval
VIKOR
Fuzzy
TOPSIS
Improved
CURLI
A1 6 6 6 6 6 5 6 5
A2 3 3 3 5 3 4 3 4
A3 2 2 2 2 2 2 2 2
A4 4 5 4 3 5 3 4 6
A5 1 1 1 1 1 1 1 1
A6 5 4 5 4 4 6 5 3
A7 7 7 7 7 7 8 7 7
A8 8 8 8 8 8 7 8 8
The comparison results reveal a high degree of correlation
between the methodologies. All approaches offer the same
optimal and secondary options. In addition, the proposed
method produces 7
th
and 8
th
alternatives similar to the other
methods. There is a variation in the arrangement of alternatives
between the 3
rd
and 6
th
. However, the difference is small, and
this does not significantly impact the overall conclusion. It is
evident that analyzing the sensitivity of the method plays an
important role in solving the MCDM problem [34]. In this
article, we inspect the sensitivity of the proposed approach by
ranking the alternatives in the case of withdrawing at least one
alternative out of the group randomly. The rank of the
alternatives then is compared to the ideal order. The term ideal
means that there is no reverse occurring if an alternative is
eliminated. In the first scenario, the worst choice A8 is
withdrawn from the calculation (Figure 1).
Fig. 1. The order of the solution after removing A8.
Fig. 2. The order of the solution after removing A5.
Fig. 3. The order of the solution after removing A4.
After that, the best alternative is eliminated from the list
(Figure 2), and finally, the alternative in the middle of the rank
is eliminated (Figure 3). It is observed that in all the considered
cases, the order of the alternatives is exactly the same as the
ideal order. This proves that the proposed method is reliable
and applicable in solving MCDM problems.
B. Case Study 2
In the second case study, the proposed method is applied to
find out the best service suppliers. Each criterion is
demonstrated by linguistic variables and the decision is made
based on 5 criteria: product quality (C1), price (C2), delivery
process (C3), service quality (C4), and past efficiency (C5).
Each criterion in an alternative row has 3 sub-options and the
meaning of linguistic variables is illustrated in Table XIV [35].
The smallest criterion C2 is the best, and for the others, the
largest is the best.
The Fuzzy TOPSIS method is applied to rank the
alternatives [35]. The statistics of this alternate ranking
approach will be compared to those of the proposed method.
Applying the improved CURLI method to estimate the
alternatives in Table XIV is the same as in the case study 1, and
the ranking results are compared to the Fuzzy TOPSIS [35] in
Table XV.
Engineering, Technology & Applied Science Research Vol. 13, No. 1, 2023, 10121-10127 10126
www.etasr.com Nguyen: The Improved CURLI Method for Multi-Criteria Decision Making
TABLE XIV. DECISION-SCORE MATRIX FOR CHOOSING SERVICE SUPPLIER [35]
Alternatives
Criteria
C1 C2 C3 C4 C5
A1 (M, G, G) (VG, M, G) (G, G, G) (SB, G, G) (G, SG, VG)
A2 (G, G, VG) (SG, G, G) (VG, VG, VG) (M, G, G) (G, G, VG)
A3 (G, G, M) (SG, VG, SG) (G, SG, SB) (G, G, G) (G, VG, SG)
M – medium; G – good; VG – very good; SG – small good; SB – small bad
TABLE XV. COMPARISON BETWEEN THE IMPROVED CURLI
AND THE FUZZY TOPSIS FOR CHOOSING THE SERVICE
SUPPLIERS
Alternatives
Methods
Fuzzy TOPSIS Improved CURLI
A1 2 2
A2 1 1
A3 3 3
It can be seen that the ranks of the alternatives of the two
methods are precisely the same: A2 is the best and A3 is the
worst alternative. This once again confirms the reliability of the
proposed method. The sensitivity analysis of the alternative
ranking is also performed and evaluated in detail. Figures 4-6
indicate the chart of the solution ranking after eliminating A1,
A2, and A3.
Fig. 4. The order of the solution after removing A1.
Fig. 5. The order of the solution after removing A2.
Fig. 6. The order of the solution after removing A3.
The comparison shows that there is no reverse phenomenon
appearing in all considered scenarios. This once again confirms
the success of the proposed improved CURLI method in the
determination of the priority order.
IV. CONCLUSION
This paper proposes the improved CURLI approach based
on the original CURLI method. Two case studies were
implemented to evaluate the methodology efficiency with
different types of variables. The ranking results are compared
to those of other methods to verify the reliability of the
proposed method. The following conclusions are drawn:
It is notable that there was no major difference between the
top and bottom positions. Additionally, the sensitivity of the
improved CURLI was examined in the case of removing
some random alternatives. The results indicate that there is
no reverse of rank in any of the considered case studies.
This is strong evidence that supports the idea that the
improved CURLI method is better than the old MCDM
when there are problems with data and uncertainty.
It is also interesting that the proposed method can rank
problems in which multiple factors influence each criterion
at an alternative level without the requirement that the input
data should be normalized or the criteria weights be
evaluated.
The improved CURLI method allows solving MCDM
problems when the factors of the criteria can be linguistic
variables or a data set. This study is the first step towards
enhancing the understanding of the CURLI method to
optimize MDCM problems.
LIST OF ACRONYMS
MCDM Multi-Criteria Decision-Making
CURLI Collaborative Unbiased Rank List Integration
MCDA Multiple-Criteria Decision Analysis
MADM Multi-Attribute Decision-Making
TOPSIS
Technique for Order Performance by Similarity to Ideal
Solution
VIKOR
Vlsekriterijumska optimizacija i KOmpromisno Resenje (in
Serbian)
MARCOS
Measurement Alternatives and Ranking according to
Compromise Solution
PEG Pareto-Edgeworth Grierson
CODAS COmbinative Distance-based ASsessment
R Ranking of the attributes and alternatives
SAW Simple Additive Weighting
WASPAS Weighted Aggregates Sum Product Assessment
MOORA Multi-Objective Optimization on the basis of Ratio Analysis
COPRAS COmplex PRroportional ASsessment
PIV Proximity Indexed Value
MABAC Multi-Attributive Border Approximation area Comparison
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