Using an Integrated Consistent Fuzzy Preference Relations and Interval
Type-2 Fuzzy Topsis Methodology for Personnel Selection and
Promotion
KEMAL GÖKHAN NALBANT
Department of Software Engineering
Beykent University
Hadim Koruyolu Street, 34936, Sariyer, Istanbul
TURKEY
ORCID-ID: 0000-0002-5065-2504
Abstract: - Promotion is an organizational procedure. Education, experience, and personal qualities are crucial
requirements for individuals to be promoted. Their characteristics determine the promotion-eligible employee's
approach to the job and compatibility with coworkers. This research employs an integrated Consistent Fuzzy
Preference Relations (CFPR) - Interval Type-2 (IT2) Fuzzy TOPSIS methodology to identify the most
competent individuals for promotion. Using this methodology, the ranking of individuals for a case study in
Turkey is calculated. The CFPR technique calculates the weight of the criteria stated by experts in our most
recent research [1]. Then, the IT2 Fuzzy TOPSIS method is used to determine the order of options using IT2
trapezoidal fuzzy numbers. Thus, the best competent candidate for promotion is selected. Thus, managers and
human resources departments may assess and promote employees rapidly.
Key-Words: - Personnel Selection, Personnel Promotion, Fuzzy Logic, Multi Criteria Decision Making
(MCDM), Consistent Fuzzy Preference Relations (CFPR), Interval Type-2 Fuzzy TOPSIS.
Received: August 6, 2021. Revised: March 25, 2022. Accepted: April 21, 2022. Published: June 3, 2022.
1 Introduction and Literature Review
Personnel selection is one of the most significant
factors in the business process. For an enterprise to
carry out its business and eliminate the lack of
personnel in places where it is disrupted, personnel
selection tries to fill that gap by choosing the most
experienced, talented, and qualified people who are
most suitable for that job or position.
Multi-criteria decision-making (MCDM) [2]
refers to selecting or ranking options from a
collection of accessible alternatives according to
numerous criteria. The MCDM methodology is
utilized for staff selection procedures. This research
tries to determine the best candidate for
advancement inside a company. The criteria for staff
selection are derived from our most current study
[1]. Consequently, the problem of people selection
is improved for this investigation. Then, the IT2
Fuzzy Topsis methodology is utilized to choose the
most qualified employees. Numerous research on
staff selection is available in the literature [3-11].
Zadeh [12] presented Type-2 fuzzy sets (T2
FSs). T2 FSs are an expansion of a standard fuzzy
set known as a Type-1 fuzzy set (T1 FS). The T2 FS
method represents uncertainty with greater
flexibility than T1 FS. In addition, uncertainty may
be adequately modeled with a T2 FS [13]. MCDM
methods are very important for decision making
problems. Many selection problems are solved by
MCDM methods. There are many studies in the
literature using MCDM methods [14-21].
The CFPR discovered by [22] simplifies pairwise
comparison. Numerous research on the CFPR
approach has been published. Patel et al. [23]
assessed risks using the CFPR approach. Lu et al.
[24] utilized CFPR for the Korean LNG Bunkering
Port site selection. Ozdemir et al. [25] analyzed
campus components using CFPR and FANP
techniques by inclusive design principles. Ozdemir
and Nalbant [9] combined the CFPR and FAHP
selection procedures.
Numerous research on the Fuzzy TOPSIS
approach using IT2 FSs may be found in the
literature. Chen and Lee [26] introduced an IT2
Fuzzy TOPSIS technique for dealing with fuzzy
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multiple-attribute group decision-making issues
based on IT2 FSs. Dymova et al. [27] created an
IT2-fuzzy modification of the TOPSIS approach
using -cuts to express IT2-fuzzy values. Liao [28]
suggested two novel TOPSIS material selection
techniques based on IT2 FSs. Buyukozkan et al.
[29] established a group decision framework for
assessing and selecting an appropriate knowledge
management solution based on the IT2 fuzzy
TOPSIS technique. Yildiz [30] used IT2 fuzzy
TOPSIS to choose the best vendor. Toklu [31]
created a model that uses the IT2 Fuzzy TOPSIS
approach to find the best suitable calibration source.
Alaoui et al. [32] suggested an IT2-fuzzy TOPSIS-
based solution for agriculture MCDM issues. Zhang
et al. [33] created an IT2 Fuzzy TOPSIS method
with a utility function and employed it to assess the
operational risk of a subway station. Bera et al. [34]
established a framework for selecting potential
suppliers using the IT2 Fuzzy TOPSIS approach.
Ozdemir et al. [35] present a novel hybrid model
based on IT2 Fuzzy Analytic Network Process
(FANP) and IT2 Fuzzy TOPSIS for evaluating store
layout options generated using a ruled-based design
technique.
In the Section 2, the integrated CFPR-IT2 Fuzzy
TOPSIS methodology is explained. In Section 3,
personnel selection problem is defined and the
integrated technique is applied to personnel
selection problem. The evaluation of the results is
given in Section 4.
2 Integrated CFPR - Interval Type-2
Fuzzy Topsis Methodology
Lee and Chen [36] introduced an approach known
as IT2 Fuzzy TOPSIS. Lee and Chen [36] defined
ranking values of trapezoidal IT2 FSs.
is the IT2 FS that can be seen in Figure 1 and is
shown as:
.
Figure 1. The membership functions of the IT2 FS
[37].
The ranking value
of the IT2 FS
is
shown below [26, 31, 36].
(1)
is the average of the elements
and
,
,
,
is the standard deviation of the elements
and
,
,
,
is the standard deviation of the elements
,
,
,
,
,
is the membership value of the element
in the trapezoidal membership function ,
, , and .
In (1), the summation of
and is
called the basic ranking score, where deducting the
average of
and from the basic ranking
score gives the dispersive IT2 Fuzzy set a
penalty, where .
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Alternatives , denotes the
number of alternatives.
Attributes , denotes the number
of attributes.
(for benefit) and (for cost)
and .
Decision-makers , denotes the
number of decision-makers.
The linguistic variables and their trapezoidal IT2
fuzzy scales of importance are listed in Table 1 [38].
Table 1. Linguistic terms [38].
Linguistic
Terms
Trapezoidal IT2 fuzzy scales
Low (L)
(0,0.1,0.1,0.3;1,1) (0.05,0.1,0.1,0.2;0.9,0.9)
High (H)
(0.7,0.9,0.9,1;1,1) (0.8,0.9,0.9,0.95;0.9,0.9)
Medium
(M)
(0.3,0.5,0.5,0.7;1,1) (0.4,0.5,0.5,0.6;0.9,0.9)
Medium
High (MH)
(0.5,0.7,0.7,0.9;1,1) (0.6,0.7,0.7,0.8;0.9,0.9)
Medium
Low (ML)
(0.1,0.3,0.3,0.5;1,1) (0.2,0.3,0.3,0.4;0.9,0.9)
Very High
(VH)
(0.9,1,1,1;1,1) (0.95,1,1,1;0.9,0.9)
Very Low
(VL)
(0,0,0,0.1;1,1) (0,0,0,0.05;0.9,0.9)
The methodological flow of the integrated CFPR-
IT2 Fuzzy TOPSIS is explained below [9, 31, 39]:
Step 1. Define the problem and decide its purpose in
light of that definition. Identify the model's primary
criteria, subcriteria, and alternatives.
Step 2. Comparison. Develop pairwise comparison
matrices based on the criteria. The decision-makers
give pairwise comparisons for n-1 preference
values.
Step 3. Transformation. Transform the preference
value
into through (2).
(2)
Then, calculate the remaining
by using (3), (4)
and (5).
(3)
(4)
(5)
This preference matrix may include values from the
interval [-a, 1+a] instead of the interval [0, 1]. To
maintain reciprocity in this circumstance, a
transformation function is employed. Finding the
transformation by (6).
(6)
Here, a represents the absolute lowest value in this
preference matrix. Similarly, fuzzy preference
relation matrices are created for all decision-makers.
Step 4. Aggregation. Aggregate the fuzzy preference
relation matrices to get the selection criteria's
important weights. Let
denote the transformed
fuzzy preference value of the -th decision maker for
criteria
i
and criteria. To incorporate the opinions
of m decision-makers, the average value approach
(7) is utilized. m represents the total amount of
decision-makers.
,
(7)
Step 5. Normalization. Normalize the aggregated
fuzzy related preference matrices. represents
each criterion's normalized fuzzy preference value
in (8), and the normalized fuzzy preference relation
matrix is determined.
(8)
Calculate the importance weight of each criteria (9).
(9)
Step 6. Build the decision matrix of the th
decision-maker and obtain the average decision
matrix (
);
where
, is an IT2 FS,
, .
Step 7. Retrieve the average weighting matrix from
the CFPR technique in Step 7.
Step 8. Find the weighted decision matrix as:
,
and .
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Step 9. The ranking value of the IT2 FS
is computed where by using (1),
, , .
Step 10. The positive ideal solution (PIS)
and the negative ideal
solution (NIS)
are calculated
as:
Step 11. Compute the distance among each
alternative and the PIS and the distance
among each alternative and the NIS as:
for .
Step 12. Calculate the closeness coefficient :
Select the best alternative.
The methodological flow diagram is shown in
Figure 2 [30, 39].
Step 1. Define the problem and decide the criteria, decision makers and alternatives.
Step 2. Construct pairwise comparison matrices.
Step 3. Find preference ralation matrices for all decision makers.
Step 4. Aggregate the fuzzy preference ralation matrices.
Step 5. Normalize the aggregated fuzzy relation matrices and calculate the importance weights of each criteria.
Step 6. Build the decision matrix and obtain the average decision matrix.
Step 7. Get the integrated (average weighting) matrix using the importance weights of each criteria calculated from CFPR.
Step 8. Obtain the weighted decision matrix.
Step 9. Find the ranking values.
Step 10. Calculate the PIS and the NIS.
Step 11. Find the distance among each alternative.
Step 12. Obtain the closeness coefficient and choose the best alternative.
Figure 2. The flow diagram of the application of
hybrid CFPR-IT2 Fuzzy TOPSIS methodology.
3 Problem Definition and Application
In this section, we studied for selecting the
personnel applying integrated CFPR-IT2 Fuzzy
TOPSIS methodology. The problem of personnel
selection for a company in Istanbul, Turkey, was
selected for this study. The company intends to
promote one of the engineers to chief engineer. We
questioned three decision-makers from the
institution and the company. Five main criteria and
22 sub-criteria were determined based on the
opinions of academicians and business managers, as
indicated in Table 2 [1]. In this new problem, 5
personnel were determined according to the
managers. One of them will be promoted.
Table 2. Personnel selection criteria[1].
Main Criteria
Subcriteria
MC1
ACTIVITY
SC11
Productive Activity
SC12
Auxiliary Activity
SC13
Inefficient Activity
MC2
FEE
SC21
Fee Paid
SC22
Payable Fee
SC23
Requested Fee
MC3
EDUCATION
SC31
Education Status
SC32
Foreign Languages
SC33
Certificates
SC34
Job Experience
SC35
Technology Usage
SC36
Lifelong Learning
MC4
INTERNAL
FACTORS
SC41
Self-Confidence
SC42
Take Initiative
SC43
Analytic Thinking
SC44
Leadership
SC45
Productivity
SC46
Decision Making / Problem
Solving
MC5
BUSINESS
FACTORS
SC51
Compatible with the Team /
Communication
SC52
Teamwork Skills
SC53
Finishing Work on Time
SC54
Business Discipline
The average weighting matrix was taken from our
previous study in Table 3 [1].
Table 3. Importance weights of subcriteria.
Main-criteria
Weight
Subcriteria
Weight
MC1
0.292
SC11
0.388
SC12
0.337
SC13
0.275
MC2
0.153
SC21
0.288
SC22
0.346
SC23
0.366
MC3
0.180
SC31
0.197
SC32
0.208
SC33
0.116
SC34
0.183
SC35
0.138
SC36
0.158
MC4
0.256
SC41
0.096
SC42
0.167
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Main-criteria
Weight
Subcriteria
Weight
SC43
0.234
SC44
0.155
SC45
0.167
SC46
0.181
MC5
0.119
SC51
0.287
SC52
0.289
SC53
0.148
SC54
0.276
To determine the ranking of options using the IT2
Fuzzy TOPSIS approach, the weighted decision
matrix shown in Table 4 is first computed. v11, v12,
v13, v14 and v15 denote the weights of Alternatives
A1, A2, A3, A4, A5 according to the subcriteria
SC11; v21, v22, v23, v24 and v25 denote the
weights of Alternatives A1, A2, A3, A4 and A5
according to the subcriteria SC12, and so on. Since
the table is very large, only the sub-criteria values of
2 main criteria are given in the Table 4.
Table 4. Weighted decision matrix.
U
L
v11
0.004
0.015
0.015
0.034
1
1
0.009
0.015
0.015
0.025
0.9
0.9
v12
0.015
0.034
0.034
0.057
1
1
0.025
0.034
0.034
0.045
0.9
0.9
v13
0.079
0.098
0.098
0.110
1
1
0.089
0.098
0.098
0.104
0.9
0.9
v14
0.057
0.079
0.079
0.098
1
1
0.068
0.079
0.079
0.089
0.9
0.9
v15
0.079
0.098
0.098
0.110
1
1
0.089
0.098
0.098
0.104
0.9
0.9
v21
0.036
0.056
0.056
0.075
1
1
0.046
0.056
0.056
0.066
0.9
0.9
v22
0.016
0.036
0.036
0.056
1
1
0.026
0.036
0.036
0.046
0.9
0.9
v23
0.043
0.062
0.062
0.079
1
1
0.052
0.062
0.062
0.070
0.9
0.9
v24
0.062
0.082
0.082
0.095
1
1
0.072
0.082
0.082
0.089
0.9
0.9
v25
0.062
0.082
0.082
0.095
1
1
0.072
0.082
0.082
0.089
0.9
0.9
v31
0.005
0.019
0.019
0.035
1
1
0.012
0.019
0.019
0.027
0.9
0.9
v32
0.024
0.040
0.040
0.056
1
1
0.032
0.040
0.040
0.048
0.9
0.9
v33
0.051
0.067
0.067
0.078
1
1
0.059
0.067
0.067
0.072
0.9
0.9
v34
0.024
0.040
0.040
0.056
1
1
0.032
0.040
0.040
0.048
0.9
0.9
v35
0.040
0.056
0.056
0.070
1
1
0.048
0.056
0.056
0.063
0.9
0.9
v41
0.006
0.013
0.013
0.022
1
1
0.010
0.013
0.013
0.018
0.9
0.9
v42
0.019
0.028
0.028
0.037
1
1
0.023
0.028
0.028
0.032
0.9
0.9
v43
0.034
0.041
0.041
0.044
1
1
0.037
0.041
0.041
0.043
0.9
0.9
v44
0.031
0.038
0.038
0.043
1
1
0.034
0.038
0.038
0.040
0.9
0.9
v45
0.022
0.031
0.031
0.038
1
1
0.026
0.031
0.031
0.034
0.9
0.9
v51
0.007
0.016
0.016
0.026
1
1
0.011
0.016
0.016
0.021
0.9
0.9
v52
0.016
0.026
0.026
0.037
1
1
0.021
0.026
0.026
0.032
0.9
0.9
v53
0.041
0.049
0.049
0.053
1
1
0.045
0.049
0.049
0.051
0.9
0.9
v54
0.023
0.034
0.034
0.044
1
1
0.028
0.034
0.034
0.039
0.9
0.9
v55
0.037
0.046
0.046
0.051
1
1
0.041
0.046
0.046
0.049
0.9
0.9
v61
0.028
0.039
0.039
0.048
1
1
0.034
0.039
0.039
0.044
0.9
0.9
v62
0.017
0.028
0.028
0.039
1
1
0.022
0.028
0.028
0.034
0.9
0.9
v63
0.024
0.035
0.035
0.045
1
1
0.030
0.035
0.035
0.040
0.9
0.9
v64
0.013
0.024
0.024
0.035
1
1
0.019
0.024
0.024
0.030
0.9
0.9
v65
0.035
0.047
0.047
0.054
1
1
0.041
0.047
0.047
0.050
0.9
0.9
Then, the ranking weighted decision matrix is
shown in Table 5.
Table 5. Ranking weighted decision matrix.
A1
A2
A3
A4
A5
SC11
3.887
3.994
4.374
4.260
4.374
SC12
4.122
4.004
4.160
4.276
4.276
SC13
3.905
4.031
4.189
4.031
4.126
SC21
3.875
3.962
4.040
4.023
3.979
SC22
3.890
3.952
4.088
3.994
4.068
SC23
4.027
3.961
4.005
3.938
4.071
SC31
3.875
3.860
3.993
3.860
4.001
SC32
3.808
3.908
4.004
3.908
4.013
SC33
3.808
3.843
3.901
3.852
3.901
SC34
3.895
3.881
3.979
3.868
3.979
SC35
3.810
3.871
3.935
3.842
3.941
SC36
3.882
3.837
3.955
3.859
3.955
SC41
3.871
3.832
3.934
3.851
3.934
SC42
3.873
4.043
3.890
4.007
4.043
SC43
3.996
4.127
3.948
4.067
4.140
SC44
3.868
3.882
4.034
3.945
4.008
SC45
3.940
4.034
3.906
3.957
3.975
SC46
3.844
3.970
4.025
3.915
4.063
SC51
3.845
3.938
3.986
3.832
3.925
SC52
3.871
3.832
3.994
3.925
3.994
SC53
3.858
3.896
3.872
3.851
3.892
SC54
3.907
3.946
3.920
3.978
3.986
The positive ideal solution (PIS)
and the negative ideal solution
(NIS)
are calculated as seen
in Table 6.
Table 6. Positive and negative ideal solution.
Positive ideal solution
Negative ideal solution
4.374
3.887
4.276
4.004
4.189
3.905
4.040
3.875
4.088
3.890
4.071
3.961
4.001
3.860
4.013
3.808
3.901
3.808
3.979
3.868
3.941
3.810
3.955
3.837
3.934
3.832
4.043
3.873
4.140
3.948
4.034
3.868
4.034
3.906
4.063
3.844
3.986
3.832
3.994
3.832
3.896
3.851
3.986
3.907
The distance among each alternative and
the PIS and the distance among each
alternative and the NIS are as seen in Table 7.
Table 7. The distance and the distance .
d+
A1
A2
A3
A4
A5
0.829
0.645
0.317
0.457
0.127
d-
A1
A2
A3
A4
A5
0.167
0.402
0.799
0.580
0.848
The closeness coefficient is determined as
seen on Table 8.
Table 8. The weights and the normalized values.
Weights
Normalized Values
CC(A1)
0.168
6.22%
CC(A2)
0.384
14.24%
CC(A3)
0.716
26.54%
CC(A4)
0.559
20.74%
CC(A5)
0.870
32.26%
Total
2.696
100.00%
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According to Table 8, the alternative weights
determined using a hybrid CFPR–IT2 Fuzzy
TOPSIS approach are 0.168, 0.384, 0.716, 0.559,
and 0.888. This indicates that the sequence is A5,
A3, A4, A2, and A1 from most significant to worst.
4 Conclusion
One of the most significant aspects of organizations
is the choice of their workforce. Businesses should
be able to select the right personnel for an open
position, taking into account the criteria for
personnel selection. The quality, quantity and
suitability of the personnel, which is the most
important element of a business, plays an active role
in the success of that business. Personnel selection
problem is a very important MCDM problem for
businesses. In this study, the problem of choosing a
person to be promoted from 5 alternatives for a
company is discussed.
This study aims to pick the most qualified
employees utilizing an integrated CFPR-IT2 Fuzzy
TOPSIS technique. As determined by the evaluation
procedure, the employees are ranked as follows:
A5>A3>A4>A2>A1, followed by the rest.
Consequently, selecting Alternative A5 for the
promotion is the most reasonable option.
When it comes to resolving issues with employee
selection, MCDM procedures provide a great deal of
convenience. In terms of work that will be done in
the future, the problem may be solved using several
MCDM approaches.
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Contribution of individual authors to
the creation of a scientific article
(ghostwriting policy)
Kemal Gokhan Nalbant conceived the presented
idea. Then, he developed the theory and designed
the model and the computational framework. After
that, he performed the computations and supervised
the findings of this work. Finally, he discussed the
results and contributed to the final manuscript.
Sources of funding for research
presented in a scientific article or
scientific article itself
The author received no financial support for the
research, authorship, and/or publication of this
article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2022.21.20
Kemal Gökhan Nalbant
E-ISSN: 2224-2872
164
Volume 21, 2022
[35] "Ozdemir, Y., Ozdemir, S., & Nalbant, K. G. (2021).
A Hybrid Methodology for Prioritizing of Store Plan
Alternatives Produced with Rule-Based Design.
International Journal of Information Technology &
Decision Making, 20(06), 1685-1709."
