VIKOR with Fuzzy TOPSIS Techniques to Investigate Nurses’ Competency in
Different Job Characteristics
Ying-chyi Chou1, C. H. Lu2, C. C. Sun3
1
Department of Business Administration, Tunghai University, 181 Taichung-kang Road,
Section 3, Taichung, Taiwan, Republic of China
2
Department of Management Science, National Chiao Tung University, 1001, Dasyure Road,
East District, Hsinchu City, Taiwan, Republic of China
3
Graduate Institue & Department of International Business, Tamkang University, 151 Yingzhuan Road, Tamsui District.,
New Taipei City 25137, Taiwan, Republic of China
(1ycchou@thu.edu.tw, 2a.sun1982@gmail.com, 3ccsun@mail.tku.edu.tw)
Abstract - This study develops an integrated model
to improve performance evaluation in the hospitals. In
this paper we show the use of the Compromise
Ranking Method, also known as the VIKOR method,
in the performance evaluation of nurses’ competency.
The method is improved by introducing the fuzzy
TOPSIS for assigning the weights of relative
importance of attributes. The study thus presents a
complete assessment model that helps managers to
identify items for improvement, while simultaneously
promoting cost and time efficiencies in nurses’
competency.
Keywords - Fuzzy Set, Nurses’ Competency,
TOPSIS, VIKOR,
I. INTRODUCTION
Along with increasingly complex clinical nursing
care requirements, comes an increasing demand for highquality manpower [1]. Many nursing skills need to be
learnt on the job. The ability of hospitals to accurately
assess and manage nurses depends on the correct
adjustments to increase work loads, along with
appropriate education and training programs. This will
help to stabilize the phenomena of a high turnover rate,
particularly among new staff nurses, who often leave
temporarily or permanently due to frustration [2].
The problem of the complexity of performance
evaluation makes the development and the application of
standard models more difficult, while at the same time
actually presents a motivation for the development of
new, more flexible models, which, again, can be adapted
to specific interest positions of those who compare the
banks. The paper shows the VIKOR and fuzzy TOPSIS
method is very appropriate for the development of such
models. It is of special interest that this method provides
the development of the multi-criteria evaluation models.
The development of clinical skills and competencies
are given a central role throughout the college education
of nurses. These skills include: nursing skills, knowledge,
attitudes and performance ability [3]. Due to the
characteristics and working environments of different
nursing units and cultures, the definitions of nursing skills
vary. This adds to the complexity of developing a skills
assessment performance tool [4]. Especially in medical
centers, as the severity and complexity of patients’
conditions are more serious than those of patients at
regional or district hospitals – training requirements for
medical center capabilities are greater. In recent years the
clinical skills of nurses are the standard used to measure
medical care, hiring and performance evaluation.
Competence refers to an individual’s overall ability.
Competence includes technical skill in professional
practice, as well as attributes such as: attitude, values,
judgmental ability and personal disposition. Competency
is a measure of an individual’s particular skill or
specialization [5]. Differentiation between the terms
competence and competency are not clearly understood
and are often used interchangeably in literature [6].
Nursing ability is assessed mainly based on their clinical
performance, whilst nurses’ non-technical attributes are
overlooked. This results in complaints from patients and
their families. Therefore a complete nursing assessment
needs to be implemented, which includes: relevant
clinical skills, knowledge, attitude and all factors that
measure a nurse’s overall competency [7].
In many countries nursing students and new staff
nurses receive senior RN training and instruction [8]. This
skills assessment does not provide a comprehensive
evaluation strategy, as it neglects the feedback of students
in the process. This results in disparities between the
skills nurses learn and their on the job performance [9].
II. METHODOLOGY
A. Participants
The primary participants in this study were
emergency department (ED) paramedics in hospitals
because their jobs are fairly difficult and require a higher
level of immediate reaction and more proficient skills
than nursing personnel in other departments. We used the
simple random sampling method to select survey
candidates and distributed questionnaires to ED
paramedics in three age groups: 22 to 29 years old, 30 to
39 years old, and 40 years old and above.
B. Questionnaire design
The questionnaire was developed based on the KSAO
model proposed by Catano [10]. The primary objective of
this questionnaire is to understand the competency of each
C. Fuzzy TOPSIS and VIKOR Methods
The VIKOR method was developed for multi-criteria
optimization of complex systems. It is an effective
technique for multi-criteria analysis and has been widely
applied in compromise ranking problems in business
management. There are also many researches adopt the
VIKOR model to investigate the complex managerial
problems. Sayadi et al. [11] extended the VIKOR method
for decision making problems with interval number.
Büyüközkan & Ruan [12] applied VIKOR method to
evaluate of software development projects. Chu et al. [13]
to demonstrate the anticipated achievements of
knowledge communities (KC) through simple average
weight (SAW), “Technique for Order Preference by
Similarity to an Ideal Solution” and “VlseKriterijumska
Optimizacija I Kompromisno Resenje” (VIKOR).
Opricovic & Tzeng [14] compared with four multicriteria
decision making methods: TOPSIS, PROMETHEE,
ELECTRE, and VIKOR and find out the best method
evaluation method is VIKOR. Tzeng et al. [15] applied
TOPSIS and VIKOR to determine the best compromise
alternative fuel mode. Opricovic & Tzeng [14] tried to
reveal and to compare the procedural basis of these two
MCDM methods, TOPSIS and VIKOR
TABLE. I
Definition of job competency assessment criteria for paramedics
General
Goal
First Level
Assessment
Criteria
Second Level
Assessment
Criteria
Education level
Knowledge（
K）
Work
experience
Professional
skills
Job competency of paramedics
paramedic. The questionnaire used the 5-point Likert
scale to assess the competency characteristics of
paramedics. Survey participants provided ratings
according to their degree of agreement with each question
item. Ratings were as follows: 1 point for strongly
disagree, 2 points for disagree, 3 points for neutral, 4
points for agree, and 5 points for strongly agree.(see
Table.1)
Independent
skills
Skill（S）
Interpersonal
skills
Communication
ability
Innovative
ability
Ability（A）
Teamwork and
corporative
spirit
Agreeable
Other
Characteristics
（O）
Diligent and
forthright
Outgoing
Emotionally
sensitive
III. RESULTS
A. Determine the linguistic weighting of each criteria
We adopt Fuzzy TOPSIS method to evaluate the
weights of different criteria. Following the construction of
Fuzzy TOPSIS model, it is extremely important that
experts fill the judgment matrix. From the viewpoint of
expert validity, the buildup of most of the
operationalizations was based on the literature that caused
them to have expert validity.
Weighting each criterion by VIKOR
Table II shows the relative weight of 12 factor of the
competitive advantage for hospital, which obtained by
Fuzzy TOPSIS method. The weights for each criterion
are: C1 (0.677), C2 (0.833), C3 (0.833), C4 (0.730), C5
(0.670), C6 (0.687), C7 (0.573), C8 (0.713), C9 (0.733), C10
(0.557), C11 (0.497) and C12 (0.577). From the Fuzzy
TOPSIS results, we can understand the first two important
factors for the competitive advantage of shopping
websites are C2 (0.833) and C3 (0.833). Moreover, the less
important factor is C11 (0.497).
Open minded
Definition of
Assessment Criteria
Graduate of
domestic and
international
nursing school
Actual years of
experience in
nursing practices
Accuracy, integrity,
and consistency of
nursing practices
Completes nursing
jobs independently
Interacts well with
other people or in
groups
Effective
communication
with people or
groups
Improves nursing
procedures or rules
to enhance work
efficiency
Cooperates with
others to complete
tasks
Easygoing and
empathizes with
others
Able to complete
the tasks delegated
or assigned by
others
Has confidence and
negotiation abilities
Demonstrates
perceptive reactions
Creative and
optimistic
TABLE II
Linguistic scales for the importance of each criterion
Linguistic variable
Corresponding triangular fuzzy number
Very low (VL)
(0.0,0.1,0.3)
Low (L)
(0.1,0.3,0.5)
Medium (M)
(0.3,0.5,0.7)
High (H)
(0.5,0.7,0.9)
Very High (VH)
(0.7,0.9,1.0)
B.
TABLE III
Weights of each criterion
BNP
Ranking
C1
(0.48,0.68,0.87)
0.677
7
C2
(0.66,0.86,0.98)
0.833
1
C3
(0.66,0.86,0.98)
0.833
1
C4
(0.54,0.74,0.91)
0.730
4
C5
(0.48,0.68,0.85)
0.670
8
C6
(0.50,0.70,0.86)
0.687
6
C7
(0.38,0.58,0.76)
0.573
10
C8
(0.52,0.72,0.90)
0.713
5
C9
(0.54,0.74,0.92)
0.733
3
C10
(0.36,0.56,0.75)
0.557
11
C11
(0.30,0.50,0.69)
0.497
12
C12
(0.38,0.58,0.77)
0.577
9
deal with families of patients and patient consultation.
This will provide a more positive, rather than defensive
response when they answer patients’ questions [18] and
[19]
.
Team spirit and a strong patient first value have a
remarkable positive effect on the psychological, social
and physical needs of patients, as part of a
multidisciplinary approach to planning and delivery of
care - which is the most important factor of nursing
performance [20]. Nurses are the front line of hospital care
providing patients with information and care, and can
improve the efficiency of professional care programs.
Nurses interact with other nurses and doctors, so a
comprehensive integrated service can be provided.
Therefore interpersonal communication skills and clinical
care have a significant correlation [21].
C. Estimating the best performance model
We evaluate six hospitals’ performance with the
consensus weights of criteria identified before, and find
out each hospital’s performance(Table.IV) and
normalized the results(Table.V)
TABLE IV
The gap-values of six hospitals
The value of Sk and Qk are shown as Table V. In this
case, we set up the values S* and Q* as 0, the values Sand Q- as 1, so as to obtain the absolute relations for the
index values Rk.
In order to understand how the Rk of each objective is
affected by V(0≦V≦1), this study respectively adopts v
= 0, v = 0.5, v = 1 to compare these index values Rk for
the control objectives before and after implementation and
presents them in Table V
Criteria
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
A1 4.3 4.2 4.3 4
3.7 4.1 3.6 4.2 3.8 3.6
Alternatives
A2 3.4 3.6 3.8 3.6 4
3.2
3.6
3.9 3.5 3.8 3.5 3.5
3.4
3
A3 4.1 3.8 4.1 3.8 3.9 3.9 3.8 3.9 3.3 3.5
3.2
3.3
A4 3
3.1
3.1
A5 2.8 3.3 3.4 3.2 3.4 3.4 3.2 3.7 3.5 3.1
3
2.9
A6 3.1 3.4 3.2 3.6 3.1 3.3 3.1 3.6 2.8 3.1
2.8
2.9
3.3 3.4 3.1 3.5 3.6 3.5 3.2 3.5 3.3
TABLE V
Normalized gap-values of six hospitals
IV. DISCUSSION
Criteria
Alternatives
As mentioned earlier a combination of
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10 C11 C12
capabilities such as, technical skill, knowledge, attitude,
level of work quality, efficiency and work performance A1 18.49 17.64 18.49 16.00 13.69 16.81 12.96 17.64 14.44 12.96 10.24 12.96
are all influential. Assessment of nursing skills and on the A2 11.56 12.96 14.44 12.96 16.00 15.21 12.25 14.44 12.25 12.25 11.56 9.00
job performance, are very important. Through accurate A3 16.81 14.44 16.81 14.44 15.21 15.21 14.44 15.21 10.89 12.25 10.24 10.89
appraisal, nursing executives can develop training A4 9.00 10.89 11.56 9.61 12.25 12.96 12.25 10.24 12.25 10.89 9.61 9.61
programs to improve patient safety and care. More A 7.84 10.89 11.56 10.24 11.56 11.56 10.24 13.69 12.25 9.61 9.00 8.41
5
complex duties such as advanced nursing (Advance
A6 9.61 11.56 10.24 12.96 9.61 10.89 9.61 12.96 7.84 9.61 7.84 8.41
Practice Nursing APN), anesthesia nursing, in patient care
assessment and communication; counseling, research,
ethical decision-making and leadership are also
TABLE VI
performance assessment factors [16] and [17].
Comparison of value Rk of six hospitals according to (v=0), (v=0.5), (v=1)
In our analysis, nursing supervisors consider past
Average
gapMax
gapexperience, professional skill, patient first value, plus the
Compromise gap-values
values
values
ability to work both independently and as a team member
(Sk + Qk)/2
Sk
Qk
the most important factors. Skills such as reading
(V＝0.5)
(V＝1)
(V＝0)
biochemical test results for specific patients and other
medical information, using evidence-based medicine,
0.000 (6)
0.000 (6)
0.0000 (6)
A1
PubMed and other databases of secondary data, enable
0.940 (4)
0.470 (4)
0.0000 (4)
A2
nurses to provide a specialized care plan for patients,
0.419 (5)
0.209 (5)
0.0000 (5)
A3
ensuring proper use of equipment with technical medical
equipment to monitor changes in a patient’s condition and Alternatives A4
1.799 (3)
0.900 (3)
0.0000 (3)
ensure accurate records are kept. Professional standards
1.900
(2)
0.950
(2)
0.0000 (2)
A5
which are continuously upgraded and updated, along with
2.000 (1)
1.000 (1)
0.0000 (1)
A6
the upgrading of standard care will enable nursing staff to
V. CONCLUSION
The performance evaluation of nurses’ competency
for hospitals must be addressed in a multi-criteria context.
In this paper, we have shown how the VIKOR method,
which introduces the multi-criteria ranking index based on
the particular measure of “closeness” to the “ideal”
solution, can be used in the performance evaluation
system. The VIKOR model allows decision-makers to
understand the gaps between alternatives and aspiredlevels in practice. It provides the most satisfactory
decision by achieving the aspired levels of the
membership goals to the extent possible in the decision
environment. We then applied the modified VIKOR
method to establish the gaps in priorities between
alternatives and aspired-levels. Finally, based on these
gaps in priorities, we provide managerial implications to
improve different carriers for satisfying the customers’
needs to achieve the aspired-level. Combining the VIKOR
method with fuzzy TOPSIS for weighting the importance
of the different criteria, allows the decision-maker to
systematically assign the values of relative importance to
the attributes based on their preferences.
In summary, the Fuzzy-Decision making approach
was used to re-evaluate the performance of various
functions related to nursing performance. The three key
factors for nursing performance are: Professional ability,
patient first value and teamwork. It is necessary for
managers and nursing staff to create a positive learning
atmosphere in the work environment. This enables
nursing staff to forward and share clinical techniques,
process-related knowledge and nursing skill, which will
significantly improve the performance of nursing and
patient care quality.
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
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