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Combining FUCA, CURLI, and Weighting
Methods in the Decision-Making of Selecting
Technical Products
Anh-Tu Nguyen
Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam
tuna@haui.edu.vn (corresponding author)
Received: 6 May 2023 | Revised: 25 May 2023 | Accepted: 2 June 2023
Licensed under a CC-BY 4.0 license | Copyright (c) by the authors | DOI: https://doi.org/10.48084/etasr.6015
ABSTRACT
Determining the optimal one from the available alternatives is useful in numerous aspects of life. The
process of selecting technical products from an available catalog also follows this pattern. This study was
carried out to select the best from two types of technical products, the ones that serve in daily life at home,
and products that are used in the agriculture field. Air conditioners and washing machines are considered
indispensable items in every household. These two types of products directly affect human lives and also
indirectly influence labor productivity. Unmanned Aerial Vehicles (UAVs) are used in numerous tasks in
the agriculture field, such as inspecting irrigation systems, checking for factors that can harm agricultural
products, etc. However, making the decision to buy one of those three types of products may become
complicated. This research was conducted to select the best alternative for each of those products. The
different types of air conditioners, washing machines, and drones considered in this study were 9, 8, and 7,
respectively. Two methods, i.e. RS (Rank Sum) and PIPRECIA (PIvot Pairwise RElative Criteria
Importance Assessment) were used to determine the weights for the criteria of each product category. The
FUCA (Faire Un Choix Adéquat) method was used in combination with the two weighting methods
mentioned above to rank the alternatives of each product category. The CURLI (Collaborative Unbiased
Rank List Integration) method was used to complete this task. So, for each product category, there will be
three different ranking results. An interesting thing has been achieved is that for each product category,
these different ranking results gave the same best solution.
Keywords-MCDM; weighting method; FUCA method; CURLI method
I. INTRODUCTION
Air conditioners and washing machines are nowadays
considered indispensable items of our daily life. They also
contribute directly to the improvement of labor productivity.
However, choosing and buying these products can be
complicated. A question that is often asked is how to buy "the
best" product among various candidate products, since for each
product, there are many different alternatives on the market.
Choosing a product based on only one or a few criteria can
easily lead to bad purchases. To choose the best product, it is
necessary to consider all the relevant criteria. This process is
termed as Multi-Criteria Decision-Making (MCDM) [1]. Such
problems also occur in the selection of UAVs for agricultural
production. However, the authors of this study can state with
certainty that up to now there have not been any studies
applying MCDM methods to select air conditioners, washing
machines, and UAVs.
Up to now, there is not an exact estimation of how many
MCDM methods there are, but certainly, they are more than
one hundred [2]. In addition, over time, new MCDM methods
are constantly being presented [3]. The MCDM methods are
divided into two groups, the first group consists of methods
that need to determine weights for the criteria, and the second
consists of methods that do not [4].
FUCA is a method that needs to determine weights for the
criteria (the first group) [5, 6]. This method has a major
difference from the methods in its class. The difference is that
it does not need to perform data normalization [5, 6]. This
method has been used for MCDM in many different fields,
such as ranking companies [7-10], selecting chemical
manufacturing process [11], selecting lathes [12], etc.
However, to the best of our knowledge, the application of the
FUCA method in selecting air conditioners, washing machines,
and UAVs has not been conducted yet. As mentioned above,
when using the FUCA method, it is necessary to determine
weights for the criteria. However, if the weights are only
determined based on the classic numerical techniques, it could
lose the objectivity of the MCDM problem as well as skip the
importance of the expert’s opinions. For household items, it is
important to consider the opinions of customers. PIPRECIA is
a criterion weighting method that considers the decision makers
opinions. Using this method, it is possible to determine criteria
weights considering the opinions of different groups of
individuals [13]. This method has also been used to calculate
the criteria weights in several fields [12-18]. However, up to
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now, this method has not been used to determine the criteria
weights for the of air conditioners, washing machines, and
UAVs. Furthermore, if only the PIPRECIA method is used to
determine the criteria weights, the question whether the ranking
results change when using a different weighting method needs
to be answered. The decision makers can have a strong belief in
an alternative when it is determined to be the best for various
weighting methods. Therefore, in addition to the PIPRECIA, in
this study, another weighting method was used, which is the RS
weighting method [19]. This is a simple method to determine
the weights for the criteria by only one formula. This method is
used to determine the criteria weights based on the decision
makers' opinion on the priority of the criteria. In recent times, it
is also applied to determine the criteria weights in various
different cases [20-25].
Using the FUCA method in combination with two
weighting methods (PIPRECIA and RS) is a solution that
belongs to the first group of the MCDM methods. Some
methods that belong to the second group are the PSI
(Preference Selection Index) method, the PEG (Pareto-
Edgeworth Grierson) method, and the CURLI method [26].
There is a difference between the CURLI method and the other
methods of this group. When using the PSI and PEG methods,
it is needed to perform data normalization, but when using the
CURLI method, the data do not need to be normalized. Which
means that when using the CURLI method, the decision
makers do not need to determine the criteria weights and
normalize data, thus eliminating the problem of choosing a
proper criteria weighting and data normalization method.
Recently, it has also been applied in MCDM in various
different aspects [26-31]. In this study, the CURLI method will
be applied to select air conditioners, washing machines, and
UAVs.
II. THE USED WEIGHTING METHODS
To calculate the weight distribution by using the RS
method, the criteria are first arranged in descending order of
priority. This arrangement is made according to the opinions of
the decision maker (buyer). After the criteria have been
arranged in a descending order, their weights are calculated
according to (1) [19]:
�� = �(��
�)�(�� ) (1)
where � is the number of criteria and
is the order of the
th
criterion.
The PIPRECIA method was used to calculate the weights
for the criteria in the following way [13]:
Step 1: Select experts (buyers) and ask their opinions on the
importance of the criteria.
Step 2: Each expert will determine the relative importance
of the criteria �� , starting from the second criterion. The
criterion’s importance is expressed as (2):
�� = �
> 1 �ℎ�� �� > ��
1 �ℎ�� �� = ��
< 1 �ℎ�� �� < ��
(2)
Step 3: For each expert, determine the coefficient ��
according to:
�� = � 1
= 12 − ��
> 1 (3)
Step 4: Determine the recalculated weights of the criteria
according to:
�� = � 1
= 1���� �
> 1 (4)
Step 5: Calculate the weights of the criteria according to the
opinion of each expert according to:
�� = ��∑ �"#"$� (5)
Step 6: Calculate the weights of the criteria according to (6)
and (7), where K is the number of experts and the index r
represents the %-th expert.
��∗ = '∏ ��)*)+ , /* (6)
�� = .�∗∑ .�∗#�$� (7)
III. THE USED MCDM METHODS
A. The FUCA Method
The steps to rank the alternatives according to the FUCA
method are [5, 6]:
Step 1: Rank the alternatives for each criterion ( %/� ).
Suppose there are m alternatives, the worst alternative will be
ranked in the m-th place and the best alternative as first.
Step 2: Calculate the score of each alternative according to:
0/ = ∑ %/� . ����+ (8)
Step 3: Rank the alternatives according to the values of 0/ .
The best alternative is the alternative with the smallest 0/ and
vice versa.
B. The CURLI Method
After having the decision matrix, the steps for ranking the
alternatives using the CURLI method include [32]:
Step 1: Scoring the alternatives for each criterion. The
scoring result of each criterion is a square matrix of level m. So
with n criteria, we will have n scoring matrices. Some
examples of scoring are:
If in the cell corresponding to column 1 and row 2, the
value 2 is better than that of 2� , the score is equal to 1,
which means 2�3 = 1.
If in the cell corresponding to column 2 and row 1, the
value of 2� is worse than that of 2 , the score is -1, which
means 2 3� = −1.
If in the cell corresponding to column 2 and row m, the
value of 2� is equal to that of 24 , the score is 0, which
means 24 3� = 0.
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Scoring is performed for all the cells that do not lie on the
main diagonal of the matrix. In the cells that lie on the main
diagonal of the matrix, the score is 0 ( 2/ 3/ = 0 ), where 6 = 1 ÷ 8. This matrix is called the scoring matrix for each
criterion (Table I).
TABLE I. A SCORING MATRIX EXAMPLE
No. P1 P2 Pi Pm
A1 A1P1 = 0 A1P2 = -1 A1Pi = … A1Pm = …
A2 A2P1 = 1 A2P2 = 0 A2Pi = … A2Pm = …
Ai AiP1 = … A1P2 = … AiPi = 0 AiPm = …
Am AmP1 = … AmP2 = 0 AmPi = … AmPm = 0
Step 2: Add all the scoring matrices for each criterion into a
single matrix. Thus, we get a matrix called the process scoring
matrix.
Step 3: Rearrange the rows and columns of the process
scoring matrix so that the new matrix has the maximum
number of cells with negative values above the main diagonal.
After rearranging, the alternative that lies on the first row is
considered as the best alternative.
IV. SELECTING THE BEST AIR CONDITIONER,
WASHING MACHINE, AND UAV
A. Air Conditioner Selection
Nine types of air conditioner of the Daikin brand were
introduced by the supplier with product codes 1HP-MSAFC-
10CRDN8, 1.5HP-GC-12IS33, 1HP-ATKC25UAVMV, 1.5HP
-RAS-H13H4KCVG-V, 1HP-FTKB25WMVMV, 1.5HP-CU/
CS-PU12XKH-8M, 1HP-CU/CS-XU9XKH-8, 1.5HP-CU/CS-
XU12XKH-8, and 1.5HP-FTKB35WMVMV. They are
denoted by A1, A2, A3, A4, A5, A6, A7, A8, and A9
alternatives, respectively. Ten criteria were used to evaluate
each type of air conditioner, including:
C1: Is the cost (dong). Dong is the currency of Vietnam, 1
USD is equivalent to about 23500 dongs.
C2: Is the effective cooling area (m�).
C3: Is the amount of electricity consumed (kW/h).
C4: Is the average cooling speed (BTU).
C5: Is the power of device (HP).
C6: Is the warranty period (month).
C7: is the maximum noise level of the indoor unit (dB).
C8: is the maximum noise level of the outdoor unit (dB).
C9: Is the weight of the indoor unit (kg).
C10: Is the weight of the outdoor unit (kg).
A survey was carried out among 6 experts to determine the
priority of the criteria. All the experts gave the same opinion.
The criteria are arranged in descending order of priority as:
C1 > C2 > C3 > C4 > C5 > C6 > C7 > C8 > C9 > C10. The
data on the types of air conditioners are summarized in Table
II. The criterion type (the larger the better, or the smaller the
better) of each criterion is also summarized in the last row of
this table. The most remarkable points from Table II are that
C1 is the smallest at A1, C2 is the largest at A6 and A8, C3 is
the smallest at A9, C4 is the largest at A4, and so on. Hence, it
is clear that the ranking could not be completed by relying
solely on the obtained data in this Table. All 10 criteria must be
considered in order to identify the optimal alternative. This is
the reason why applying MCDM methods is essential.
TABLE II. TYPES OF AIR CONDITIONER
No. C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
A1 6590000 15 1.1 9000 1 36 39 51.5 7.4 21.7
A2 7390000 20 1.3 4095 1.5 36 32 50 8.5 21
A3 11590000 45 0.68 8500 1 12 38 47 8 23
A4 11990000 20 1.18 12000 1.5 24 24 48 9 21
A5 10990000 15 0.82 8500 1 12 36 47 8 19
A6 13890000 60 1.07 11900 1.5 12 28 48 8 23
A7 13490000 45 0.68 8700 1 12 19 47 10 18
A8 16890000 60 0.95 11900 1.5 12 19 48 10 23
A9 13490000 20 0.6 11900 1.5 12 37 47 8 22
Type Min Max Min Max Max Max Min Min Min Min
Equation (1) was applied to calculate the weights of the
criteria according to the RS method. Accordingly, the weights
of the criteria C1, C2, C3, C4, C5, C6, C7, C8, C9, and C10
have the values of 0.2929, 0.1929, 0.1429, 0.1096, 0.0846,
0.0646, 0.0479, 0.0336, 0.0211, and 0.0100, respectively. To
calculate the weights according to the PIPRECIA method, a
survey was also carried out with the opinions of 6 experts and
(2) was used. Table III is a summary of experts’ opinions on
the relative importance of the criteria.
Applying the (3)-(7), the weights of the criteria were
determined as shown in Table IV. Step 1 of the FUCA method
was applied to rank the alternatives for each criterion. The
results are summarized in Table V. Step 2 of the FUCA method
was applied to calculate the score for each alternative with two
different sets of weights (8). The results were summarized in
Table VI. Step 3 of the FUCA method was applied to rank the
alternatives. The results are summarized in Table VI.
Step 1 of the CURLI method was applied to score the
alternatives for each criterion. The results are presented in
Tables VII - XVI. The process scoring matrix was determined
by applying the step 2 of the CURLI method as shown in Table
XVII. The process scoring matrix was rearranged according to
step 3 of the CURLI method, and the results were shown in
Table XVIII.
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TABLE III. EXPERT OPINIONS ON THE RELATIVE IMPORTANCE OF THE CRITERIA ��
Criteria Expert 1 Expert 2 Expert 3 Expert 4 Expert 5 Expert 6
C1
C2 0.98 0.9 0.8 0.9 0.98 0.9
C3 0.96 0.96 0.96 0.9 1 1
C4 0.95 0.95 0.95 0.95 0.95 1
C5 0.94 0.94 0.9 0.9 0.95 0.94
C6 0.93 0.92 0.92 0.92 0.93 0.93
C7 0.9 0.9 0.9 0.9 0.9 0.9
C8 0.89 0.89 0.89 0.8 0.89 0.89
C9 0.85 0.6 0.5 0.8 0.8 0.75
TABLE IV. THE WEIGHTS OF THE CRITERIA DETERMINED USING THE PIPRECIA METHOD
Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
Weight 0.1370 0.1259 0.1215 0.1167 0.1089 0.1013 0.0921 0.0819 0.0641 0.0508
TABLE V. RANKING THE ALTERNATIVES OF EACH CRITERION
No. C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
A1 1 8.5 7 5 7.5 1.5 9 9 1 5
A2 2 6 9 9 3 1.5 5 8 6 3.5
A3 4 3.5 2.5 7.5 7.5 6.5 8 2.5 3.5 8
A4 5 6 8 1 3 3 3 6 7 3.5
A5 3 8.5 4 7.5 7.5 6.5 6 2.5 3.5 2
A6 8 1.5 6 3 3 6.5 4 6 3.5 8
A7 6.5 3.5 2.5 6 7.5 6.5 1.5 2.5 8.5 1
A8 9 1.5 5 3 3 6.5 1.5 6 8.5 8
A9 6.5 6 1 3 3 6.5 7 2.5 3.5 6
TABLE VI. ALTERNATIVE SCORE AND RANKING WITH
THE FUCA METHOD
No.
RS weight PIPRECIA weight
vi Rank vi Rank
A1 5.4545 8 5.4927 9
A2 5.3455 7 5.3288 7
A3 5.0182 6 5.2138 6
A4 4.6455 2 4.5532 2
A5 5.6182 9 5.3998 8
A6 4.7636 3 4.8387 4
A7 4.8636 5 4.7480 3
A8 4.8000 4 4.9445 5
A9 4.4909 1 4.4803 1
TABLE VII. ALTERNATIVES SCORE FOR CRITERION C1
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 -1 -1 -1 -1 -1 -1 -1
A2 1 0 -1 -1 -1 -1 -1 -1 -1
A3 1 1 0 -1 1 -1 -1 -1 -1
A4 1 1 1 0 1 -1 -1 -1 -1
A5 1 1 -1 -1 0 -1 -1 -1 -1
A6 1 1 1 1 1 0 1 -1 1
A7 1 1 1 1 1 -1 0 -1 0
A8 1 1 1 1 1 1 1 0 1
A9 1 1 1 1 1 -1 0 -1 0
TABLE VIII. ALTERNATIVES SCORE FOR CRITERION C2
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 1 1 1 0 1 1 1 1
A2 -1 0 1 0 -1 1 1 1 0
A3 -1 -1 0 -1 -1 1 0 1 -1
A4 -1 0 1 0 -1 1 1 1 0
A5 0 1 1 1 0 1 1 1 1
A6 -1 -1 -1 -1 -1 0 -1 0 -1
A7 -1 -1 0 -1 -1 1 0 1 -1
A8 -1 -1 -1 -1 -1 0 -1 0 -1
A9 -1 0 1 0 -1 1 1 1 0
TABLE IX. ALTERNATIVES SCORE FOR CRITERION C3
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 1 -1 1 1 1 1 1
A2 1 0 1 1 1 1 1 1 1
A3 -1 -1 0 -1 -1 -1 0 -1 1
A4 1 -1 1 0 1 1 1 1 1
A5 -1 -1 1 -1 0 -1 1 -1 1
A6 -1 -1 1 -1 1 0 1 1 1
A7 -1 -1 0 -1 -1 -1 0 -1 1
A8 -1 -1 1 -1 1 -1 1 0 1
A9 -1 -1 -1 -1 -1 -1 -1 -1 0
TABLE X. ALTERNATIVES SCORE FOR CRITERION C4
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 -1 1 -1 1 -1 1 1
A2 1 0 1 1 1 1 1 1 1
A3 1 -1 0 1 0 1 1 1 1
A4 -1 -1 -1 0 -1 -1 -1 -1 -1
A5 1 -1 0 1 0 1 1 1 1
A6 -1 -1 -1 1 -1 0 -1 0 0
A7 1 -1 -1 1 -1 1 0 1 1
A8 -1 -1 -1 1 -1 0 -1 0 0
A9 -1 -1 -1 1 -1 0 -1 0 0
According to the data in Table XVIII, the ranking order of
the alternatives is: A9 > A6 > A8 > A3 > A4 > A7 > A1 > A2
> A5. Figure 1 shows the ranking results of the air conditioners
using the FUCA method and the CURLI method.
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TABLE XI. ALTERNATIVES SCORE FOR CRITERION C5
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 1 0 1 0 1 0 1 1
A2 -1 0 -1 0 -1 0 -1 0 0
A3 0 1 0 1 0 1 0 1 1
A4 -1 0 -1 0 -1 0 -1 0 0
A5 0 1 0 1 0 1 0 1 1
A6 -1 0 -1 0 -1 0 -1 0 0
A7 0 1 0 1 0 1 0 1 1
A8 -1 0 -1 0 -1 0 -1 0 0
A9 -1 0 -1 0 -1 0 -1 0 0
TABLE XII. ALTERNATIVES SCORE FOR CRITERION C6
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 0 -1 -1 -1 -1 -1 -1 -1
A2 0 0 -1 -1 -1 -1 -1 -1 -1
A3 1 1 0 1 0 0 0 0 0
A4 1 1 -1 0 -1 -1 -1 -1 -1
A5 1 1 0 1 0 0 0 0 0
A6 1 1 0 1 0 0 0 0 0
A7 1 1 0 1 0 0 0 0 0
A8 1 1 0 1 0 0 0 0 0
A9 1 1 0 1 0 0 0 0 0
TABLE XIII. ALTERNATIVES SCORE FOR CRITERION C7
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 1 1 1 1 1 1 1 1
A2 -1 0 -1 1 -1 1 1 1 -1
A3 -1 1 0 1 1 1 1 1 1
A4 -1 -1 -1 0 -1 -1 1 1 -1
A5 -1 1 -1 1 0 1 1 1 -1
A6 -1 -1 -1 1 -1 0 1 1 -1
A7 -1 -1 -1 -1 -1 -1 0 0 -1
A8 -1 -1 -1 -1 -1 -1 0 0 -1
A9 -1 1 -1 1 1 1 1 1 0
TABLE XIV. ALTERNATIVES SCORE FOR CRITERION C8
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 1 1 1 1 1 1 1 1
A2 -1 0 1 1 1 1 1 1 1
A3 -1 -1 0 -1 0 -1 0 -1 0
A4 -1 -1 1 0 1 0 1 0 1
A5 -1 -1 0 -1 0 -1 0 -1 0
A6 -1 -1 1 0 1 0 1 0 1
A7 -1 -1 0 -1 0 -1 0 -1 0
A8 -1 -1 1 0 1 0 1 0 1
A9 -1 -1 0 -1 0 -1 0 -1 0
TABLE XV. ALTERNATIVES SCORE FOR CRITERION C9
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 -1 -1 -1 -1 -1 -1 -1
A2 1 0 1 -1 1 1 -1 -1 1
A3 1 -1 0 -1 0 0 -1 -1 0
A4 1 1 1 0 1 1 -1 -1 1
A5 1 -1 0 -1 0 0 -1 -1 0
A6 1 -1 0 -1 0 0 -1 -1 0
A7 1 1 1 1 1 1 0 0 1
A8 1 1 1 1 1 1 0 0 1
A9 1 -1 0 -1 0 0 -1 -1 0
It can be seen from Figure 1 that the ranking orders of the
alternatives are not completely the same when using FUCA and
CURLI. The ranking orders of the alternatives are also not the
same when using RS and PIPRECIA. This issue is consistent
with the findings in [1]. However, in every performed case, A9
is always ranked as 1
st
. Accordingly, among the 9 considered
types of air conditioners, the 1.5HP-FTKB35WMVMV is
determined to be the best.
TABLE XVI. ALTERNATIVES SCORE FOR CRITERION C10
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 1 -1 -1 1 -1 1 1
A2 1 0 1 0 -1 1 -1 1 1
A3 -1 -1 0 -1 -1 0 -1 0 -1
A4 1 0 1 0 -1 1 -1 1 1
A5 1 1 1 1 0 1 -1 1 1
A6 -1 -1 0 -1 -1 0 -1 0 -1
A7 1 1 1 1 1 1 0 1 1
A8 -1 -1 0 -1 -1 0 -1 0 -1
A9 -1 -1 1 -1 -1 1 -1 1 0
TABLE XVII. THE PROCESS SCORING MATRIX
No. P1 P2 P3 P4 P5 P6 P7 P8 P9
A1 0 -1 1 0 -2 4 -1 4 4
A2 1 0 2 1 -2 5 0 3 2
A3 -1 -2 0 -2 -1 1 -1 0 1
A4 0 -1 2 0 -2 0 -2 0 0
A5 2 2 1 2 0 2 1 1 3
A6 -4 -5 -1 0 -2 0 -1 0 0
A7 1 0 1 2 -1 1 0 1 3
A8 -4 -3 0 0 -1 0 -1 0 1
A9 -4 -2 -1 0 -3 0 -3 -1 0
TABLE XVIII. THE PROCESS SCORING MATRIX AFTER
REARRANGEMENT
No. P9 P6 P8 P3 P4 P7 P1 P2 P5
A9 0 0 -1 -1 0 -3 -4 -2 -3
A6 0 0 0 -1 0 -1 -4 -5 -2
A8 1 0 0 0 0 -1 -4 -3 -1
A3 1 1 0 0 -2 -1 -1 -2 -1
A4 0 0 0 2 0 -2 0 -1 -2
A7 3 1 1 1 2 0 1 0 -1
A1 4 4 4 1 0 -1 0 -1 -2
A2 2 5 3 2 1 0 1 0 -2
A5 3 2 1 1 2 1 2 2 0
Fig. 1. Ranking of the air conditioner types.
B. Washing Machine Selection
Eight types of washing machines were introduced by the
supplier with product codes WW80T3020WW/SV,
WA90T5260BY/SV, WW95TA046AX/SV, WW10T634DLX/
SV, WW10TA046AE/SV, WW90T634DLN/SV, WA12T53
60BV/SV, and WA10T5260BV/SV. They are denoted by A1,
A2, A3, A4, A5, A6, A7, and A8 alternatives, respectively. The
12 criteria used to evaluate each alternative were arranged in
descending order of priority:
0
1
2
3
4
5
6
7
8
9
10
A1 A2 A3 A4 A5 A6 A7 A8 A9
FUCA + RS
FUCA + PIPRECIA
CURLI
R
a
n
k
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C1: Is the mass of τηε fabric that can be processed in one
wash (kg).
C2: Is the cost (dong).
C3: Is the efficiency of electricity use (Wh/kg).
C4: Is the maximum spin speed (rev/min).
C5: Is the engine warranty period (years).
C6: Is the cover material (Stainless Steel = SS, Powder
Coated Metal = PCM). According to experts’ opinions, SS
is better than PCM.
C7: Is the weight (kg).
C8: Is the height (cm).
C9: Is the width (cm).
C10: Is the depth (cm).
C11: Is the length of the water supply pipe (cm).
C12: Is the length of the drainpipe (cm).
The data for the 8 washing machines are summarized in
Table XIX. Each criterion type (the larger the better, or the
smaller the better) is also listed in the last row. According to
the data in Table XIX, C1 is the largest at A7, C2 is the
smallest at A2, C3 is the smallest at A7, C4 is the largest at A4-
A6, etc. This demonstrates that MCDM methods are highly
recommended for identifying the best alternative in this
problem. The relative importance between the criteria was also
obtained by surveying the opinions of 6 experts. The results are
summarized in Table XX. The weights of the criteria were
calculated according to both RS and PIPRECIA and are
summarized in Table XXI.
TABLE XIX. WASHING MACHINE TYPES
No. C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
A1 8 6990000 12.6 1200 11 SS 58 83.7 59.5 49.3 106 165
A2 9 5990000 10.6 700 20 PCM 40 105 61 67.5 109 121
A3 9.5 10290000 11.9 1400 20 SS 65 84.3 60 60 212 145
A4 10 10990000 13.1 1400 20 SS 67 85 60 60.6 211 154
A5 10 8790000 13.1 1400 20 SS 65 85 60 55 195 140
A6 9 9990000 13 1400 20 PCM 67 84.2 60 61.5 214 131
A7 12 8390000 7.2 700 20 PCM 43 109 61 65.5 106 115
A8 10 7190000 8.8 700 20 PCM 41 108 60 65 106 115
Type Max Min Min Max Max SS is better than PCM Max Max Max Max Max Max
TABLE XX. EXPERTS’ OPINION ON THE RELATIVE IMPORTANCE OF THE CRITERIA S;
Criteria Expert 1 Expert 2 Expert 3 Expert 4 Expert 5 Expert 6
C1
C2 0.98 0.99 0.92 0.97 0.92 0.9
C3 0.94 0.95 0.94 0.92 0.97 0.95
C4 0.92 0.92 0.92 0.92 0.95 0.95
C5 0.97 0.98 0.98 0.95 0.95 0.95
C6 0.97 0.94 0.92 0.92 0.92 0.92
C7 0.96 0.96 0.96 0.94 0.94 0.94
C8 0.95 0.95 0.99 0.92 0.95 0.95
C9 0.99 0.92 0.92 0.92 0.92 0.92
C10 0.89 0.89 0.89 0.85 0.96 0.96
C11 0.88 0.9 0.9 0.85 0.9 0.95
C12 0.98 0.8 0.9 0.85 0.9 0.95
TABLE XXI. CRITERIA WEIGHTS
Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
RS Weight 0.1538 0.1410 0.1282 0.1154 0.1026 0.0897 0.0769 0.0641 0.0513 0.0385 0.0256 0.0128
PIPRECIA weight 0.1120 0.1064 0.1008 0.0942 0.0909 0.0851 0.0811 0.0773 0.0724 0.0663 0.0601 0.0535
Ranking of the washing machines is conducted with steps
similar to those of the precious section. The results are
illustrated in Figure 2. Observing Figure 2, it can be seen that
the ranking orders of the alternatives are not completely the
same when using FUCA and CURLI. The ranking orders of the
alternatives are also not completely the same when using the
weighting methods RS and PIPRECIA. However, all the cases
determined that A7 is the 1
st
alternative and A1 ranked 8
th
.
Accordingly, WA12T5360BV/SV is the best type and
WW80T3020WW/SV is the worst type among the 8
considered washing machines. After ranking the two product
categories (air conditioner, washing machine) we can see that
the best alternative determined by the CURLI method is always
similar to the one determined when using the FUCA method.
Also, when using the FUCA method to determine the best
alternative, that alternative does not depend on the weights for
the criteria.
C. UAV Selection
Seven types of agricultural UAVs were considered [33-39].
Their models are: U25L-4, U30L-6, D16L-4, U50 Max, D72L-
8, Agras T40, and Agras T30. They are designated as the
alternatives A1, A2, A3, A4, A5, A6, and A7. Nine criteria are
applied to evaluate each alternative. The criteria include
Engineering, Technology & Applied Science Research Vol. 13, No. 4, 2023, 11222-11229 11228
www.etasr.com Nguyen: Combining FUCA, CURLI, and Weighting Methods in the Decision-Making of Selecting …
Maximum takeoff weight (Kg), Aircraft weight (Kg), Aircraft
medicine box capacity (lt), Flight Altitude (m), Max Fly Time
(unloaded) (mins), Fly Time (loaded), Max Spray Width (m),
Max Spray Flow (lt), Min Spray Efficiency (hct/h). These
criteria are denoted by C1-C9, in that order. Among these
criteria, C2 is defined as the cost factor; the remaining 8 criteria
are defined as the benefit factors. The specific data of the
UAVs are indicated in Table XXII. The opinions of six experts
on the relative importance of the criteria were obtained. The
results of the survey are summarized in Table XXIII.
Fig. 2. Ranking of the washing machine types.
TABLE XXII. UAV SPECIFICATION [33-39]
No. C1 C2 C3 C4 C5 C6 C7 C8 C9
A1 51 19 25 30 25 13 8 12 10
A2 66.5 24 30 30 30 13 12 10 10
A3 36 15 16 30 25 13 8 8 5
A4 82 42 40 30 20 15 10 4.5 6.8
A5 147 52 72 30 25 13 15 5 10
A6 90 50 40 45 18 6 11 12 10
A7 65 26.3 25 45 20.5 7.8 11 12 10
TABLE XXIII. EXPERT OPINION ON THE RELATIVE
IMPORTANCE OF THE CRITERIA SJ
Criteria
Expert
1
Expert
2
Expert
3
Expert
4
Expert
5
Expert
6
C1
C2 0.98 0.97 0.99 0.97 0.97 0.94
C3 0.99 0.9 0.95 0.92 0.97 0.97
C4 0.96 0.95 0.99 0.9 0.92 0.95
C5 0.98 0.96 0.98 0.9 0.92 0.98
C6 1 0.99 0.97 0.95 0.95 1
C7 0.92 0.91 0.9 0.99 0.9 0.92
C8 0.98 1 0.91 0.92 0.95 0.95
C9 0.92 0.9 1 0.99 0.98 0.9
TABLE XXIV. CRITERIA WEIGHTS
Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9
RS Weight 0.2000 0.1778 0.1556 0.1333 0.1111 0.0889 0.0667 0.0444 0.0222
PIPRECIA weight 0.1314 0.1276 0.1215 0.1153 0.1102 0.1077 0.1001 0.0955 0.0909
Fig. 3. The UAV ranking results based on different MCDM methods.
RS and PIPRECIA were used to calculate the weights of
the criteria. The results are presented in Table XXIV. The
ranking of alternatives in this case is implemented in the same
way as above, and the results are illustrated in Figure 3. Figure
3 shows that the ranking results of the UAVs are similar.
Specifically, the combination of the FUCA method and the
PIPRECIA method gives ranking results that are completely
consistent with those of the CURLI method. This result gives
us a solid conclusion that A2 is the best alternative and A3 is
the worst. Accordingly, out of the 7 surveyed UAV types, the
U30L-6 is determined to be the best.
V. CONCLUSION
Ranking the alternatives to determine the best ones for three
product categories, namely air conditioners, washing machines,
and UAVs was carried out for the first time in this study. Four
methods including RS, PIPRECIA, FUCA, and CURLI were
applied simultaneously to accomplish this task. The main
findings of this study are:
The best found alternative is the same regardless of the
method used.
Among the considered alternatives, 1.5HP-
FTKB35WMVMV was the best air conditioner type.
The WA12T5360BV/SV is the best out of eight candidate
washing machines.
The U30L-6 is the best alternative among the seven types of
UAVs considered.
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