Content uploaded by Sayem Ahmed
Author content
All content in this area was uploaded by Sayem Ahmed on Dec 14, 2019
Content may be subject to copyright.
International Journal of Applications of Fuzzy Sets and Artificial Intelligence
(ISSN 2241-1240), Vol. 9 (2019), 60-77
A comprehensive study of Fuzzy TOPSIS
methodology for ranking of critical factors in
evaluating employee performance
1 Inzamam Ul Haq, 2 Sayem Ahmed
1 Lecturer of Industrial and Production Engineering
Department of Mechanical & Production Engineering
Ahsanullah University of Science & Technology, Dhaka-1208, Bangladesh.
E-mail: inzi.ipe61@gmail.com
2 Assistant Professor of Industrial and Production Engineering
Department of Mechanical & Production Engineering
Ahsanullah University of Science & Technology, Dhaka-1208, Bangladesh.
E-mail: sayeemahmed64@gmail.com
Abstract
Performance evaluation has become a very essential aspect in human
resource management for the efficacious management of modern
organization, staff motivation, attitude, and behavioral development.
This literature addresses this issue in the context of measuring the
performance of manufacturing plant employees in Bangladesh by
using multi-criteria decision-making techniques (MCDM).
Researches on (MCDM) has developed rapidly and has become a key
genre of research area for dealing with complex decision problems.
Studies presented in this paper propose the implementation of Fuzzy
TOPSIS as MCDM technique to aid the employee selection and
evaluation process. Fuzzy TOPSIS considers the interdependency
between criteria and weighting the importance of the different criteria
according to the decision-makers preferences to assign values for
quantification. The performance indices of employees considering
their respective performance in various evaluation criteria have been
determined and there on selecting the best employee holding the
highest performance index. The results show that this method is
suitable for the problem of performance evaluation, particularly to
supporting group decision-making. Thus, this literature enables
decision analysts with accurate, effective, and systematic decision
support tool to better understand the complete evaluation process and
choose more effective approaches for employee evaluation.
Keywords: Fuzzy TOPSIS, MCDM, Performance Evaluation,
Selection of Employee.
1. Introduction
The efficient and effective operation of an organization resides majorly on the
selection of critical factors in determining the level of performance of employees
61
A comprehensive study of Fuzzy TOPSIS ....
and thus provide a path for future expansion. Therefore, the behavior of
organization culture and its influence on the performance is crucial which depends
on the knowledge base of the critical performance factors (Audit Commission for
Local Authorities 2000). In general the indicators of performance can be considered
as measure of effectiveness and efficiency. In this circumstance, these two terms
should be clearly diversified as they may be used interchangeably in most cases and
in some cases mistakenly so but this one is not among them. Effectiveness is a
measure of the level of agreement between the target value and the obtained
outcome. Whereas efficiency is a measure of the ratio between output to input as in
envelopment of data analysis (DEA) (Meredith 1992 [1], Vonderembse and White
1995) [2]. To simplify, doing the right work is effectiveness and efficiency is doing
it right (Chase and Aquilano 1992) [3]. Hence, effectiveness is a parameter for
strategic planning which should be taken into consideration for long-term decision-
making, whereas efficiency is a parameter for operational planning which should
be taken into consideration for short-term decision-making. The degree of
achieving the desired organizational objective with targeted efficiency and
effectiveness rests on the fact that it gets the right output in the right way within
predetermined specified timeline. The measurement of performance is the
quantification of the effectiveness and efficiency of an action (
Neely et al. 1995)
[4]. It may seem to be appealing that the concept of combining the efficiency and
effectiveness to measure the level of performance of an organization, but some
researcher do disagree (Ammons 1996 [5], Berman 1998 [6]). They opinioned that
quantitative measurements provide a much more reliable measure of performance
of an organization. The cases where the inputs and outputs are quantitative are more
suitable for implementation of the latter view. However, these days’ customers’
perceived view of how an organization is performing depends on the qualitative
measures. Hence, studies portraying the level of success of an organization should
provide quantitative as well as qualitative measure to become an all-around richer
and multi-dimensional research which will be well received by the manufacturing
sector organizations.
In this day and age, the fact is reflected by the evaluation of performance of an
organization is based on the customer satisfaction which is intern an outcome in
this scenario. On the contrary, effectiveness on the basis of qualitative measures is
62
Haq & Ahmed
a much more comprehensive indicator of better performance in an organization is
suggested by some researchers (Hershey and Blanchard 1969) [7]. This view should
be considered shortsighted and biased towards the qualitative measures where
quantitative measures have been completely ignored. An organization should
consider both the effectiveness and efficiency in its measure of performance based
on both qualitative measures and quantitative measures if it aims to be world class
(Sahay 2005) [8]. Solving problems of decision making in real world for both
service as well as manufacturing systems requires more than a single performance
measurement based on different criterion because the problem is much more
complex to be defined only by optimum decision. For real systems, an approach
based on unidimensional criterion cannot lend a solution which may be measurable
and evaluable, and in some cases may even produce impractical decisions. Thus,
Multiple Criteria Decision Making (MCDM) methods have been implemented to
efficiently evaluate and measure any system (Triantaphyllou 2000) [9]. In solving
any problems based on MCDM, the basic steps are as follows- system evaluating
criteria establishment for achieving goals; generation of alternatives; assessment of
alternatives based on criteria; implementation of multi criteria decision making
method; establishing and ranking of alternatives from most acceptable to
completely or partially unacceptable; and lastly collecting an entire data set in case
of an unrealistic solution, therefore repeating all steps. MCDM is a qualitative
performance measurement approach which requires the consistency of criteria with
the system goals and decision makers that should produce true information.
Literatures based on different methods of MCDM have been illustrated (Hwang and
Yoon 1981) [10]. In classical MCDM techniques, the importance weightages and
ratings are assumed to be precisely known.
The work presented in this literature provides Fuzzy TOPSIS methodology for
performance measurement based on both qualitative and quantitative measures
which are applied in conjunction for the evaluation of performance of a reputed
manufacturing company situated in Dhaka. This research work also produces an out
of the box framework which determines manufacturing system performance to a
substantial degree. To achieve a set of strategic decisions concerning provisions for
manufacturing companies this work of research is conducted. There are two basic
approaches for measuring performance in general; one is to implement parametric
63
A comprehensive study of Fuzzy TOPSIS ....
methods where function of production is assumed to be known or statistically
estimated- such as ordinary least squares, stochastic frontier analysis, etc. The other
approach implements a non-parametric methods where the model is based on inputs
and outputs observed empirically- such as work measurement methods, AHP
(analytic hierarchy process), output/input ratios, quality plus techniques,
performance measurement matrix, balanced-scored card, practice variations studies,
DEA, performance prism, activity based costing, results and determinants structure,
performance pyramid, reporting technique, strategic measurement analysis,
performance measurement questionnaire, Malcolm Baldridge criteria for
performance excellence and theory of constraints, etc which are the majorly
implemented measurement methods of performance (McLaughlin and Coffey 1990
[11], Ghalayani and Noble 1996) [12]. Gomes et al. (2004) [13] provides a much
more elaborated picture on parametric and non-parametric approaches. Simar and
Wilson (2008) [14] investigated and analyzed DEA and FDH (free disposal hull)
by implementing bootstrap methods based on statistics although there may be some
open issues and problems. The method is applicable of theoreticians but not for
practitioners. In this work, a hybrid tool which combines two non-parametric
methods namely the fuzzy and TOPSIS are implemented to recognize which critical
factors have the most influence in determining performance of an employee and
order them according to the best to worst in a reputed manufacturing company in
Bangladesh.
2. Literature Review
The field of performance appraisal has immense opportunity of research work in
evaluating personnel management. Quite a few methods of quantitative and
judgmental measure based on this field have developed in the last decade or so. The
relationship between the level of employee performance and the performance of the
organization is truly significant and can never be overstated; this topic is illustrated
in the literature (Kilduff et al. [15], 2000; Higgs, 2005) [16]. Fuzzy synthetic
decision approach has been implemented by Ying-Feng and Ling-Show (2002) [17]
for the lecturers of universities of Taiwan for measuring performance. Kciuk (2007)
[18] illustrated a development program of personnel management in recent years.
64
Haq & Ahmed
The major concern was on the selection of workers with appropriate method of
choice for the selection and recruitment preceded by the planning of needs of
personnel. From this research it is clearly evident that the choice of workers is a
running process and requires establishment of flexibility to the ever changing needs
of any organization.
A Multiple Criteria Decision-Making approach based on Fuzzy logic is proposed
by Wua et al. (2009) [19] for evaluating banking performance in which MCDM
analytical tools of SAW, TOPSIS, and VIKOR were, respectively have been
adopted to order the performance of banking and to improve the disagreements with
three banks to portray an empirical example. An FAHP based evaluation of
performance model has been developed by Sun (2010) [20] and provide a technique
for performance of order by similarity to ideal solution, the fuzzy TOPSIS had the
arbitrary and subjectivity which are dealt with via linguistic valued that
parameterize the triangular fuzzy numbers.
TOPSIS method considers multiple criteria to recognize an ideal solution among a
finite set of points (Hwang and Yoon 1981) [10]. The principle in its basic form
states that the ideal solution should have the ‘shortest’ distance from the solution of
positive ideal point and ‘farthest’ distance from the negative ideal point. A broad
no. of studies of various aspects related with different areas on the TOPSIS method
has been discussed (Parkan and Wu 1999 [21], Deng et al. 2000 [22], Jee and Kang
2000 [23]). Hence, a combined methodology of Fuzzy TOPSIS is considered for
this research. For solving decision making problem under a group is substantially
appropriate for Fuzzy TOPSIS method in a fuzzy environment.
Among various MCDM methods the fuzzy TOPSIS is 23% higher in terms of
effectieveness than AHP, 17 % higher than Fuzzy optimum, and 11% higher than
TOPSIS finally 10 % higher than the Gray relation analysis (Wang et al. 2007) [24].
Hence TOPSIS is about 12% more effective than AHP. In this research, the
personnel employment record evaluation based on fuzzy TOPSIS with linguistic
variables is much simpler than the fuzzy AHP because process of evaluation
requires more time. These benefits are the driving force for why the algorithm is
chosen. To order the performance of banking and improve the disagreements Wu,
Tzeng, and Chen (2009) [25] applied three MCDM analytical tools of, TOPSIS,
65
A comprehensive study of Fuzzy TOPSIS ....
SAW and VIKOR as an empirical example. However, Vicor method has been
observed to have a better assessment method in evaluating banking performance.
Based on a combined method of AHP and VIKOR, Kaya and Kahraman (2011) [26]
researched on Fuzzy multiple criteria forestry decision making problem.
Recognizing and selecting the most appropriate alternative among various
alternatives is a problem of multi-criteria decision-making (MCDM). Among the
widely available methodologies applicable in various fields like business,
engineering and science, MCDM is of the most acceptable one. It has been
developed to make the process more rational, explicit and efficient by improving
the decision making quality (Y. Deng et al. 2011[27] and M. Noor-E-Alam 2011
[28]). In a typical problem of MCDM it involves evaluation of a number of
alternatives based on a number of criteria which has appropriate relationship to
evaluate these alternatives. Compromising the evaluating solution of best
alternative from a set of available alternatives based on objectives are the commonly
dealt problems of MCDM.
Presently, researcher of different field have prospected various MCDM: TOPSIS
(Technique for Order Preference by Similarity to Ideal Solution) (Wu, Tzeng, and
Chen (2009) [25], VIKOR (VIsekriterijumska Optimizacija i KOmpromisno
Resenje: multicriteria optimization and compromise solution) (S. Opricovic and G.-
H. Tzeng 2004) [29], AHP (Analytic Hierarchy Process) (T. L. Saaty 2006) [30],
and DEA (Data Envelopment Analysis) (H.-T. Lin 2010) [31]. Due to arbitrary
characteristics of the input data and ambivalence of decision-making process, a
theory based on fuzzy set has been implemented into MCDM technique by various
researchers for employee evaluation problem. From this pool of methodologies,
VICOR and TOPSIS methods are the most appropriate ones to solve the problem
of personnel selection as these have the capacity to comprehend and deal with each
and every form of judgement criteria, which have clarity of outcomes and simplicity
to deal with criteria and decision alternatives (R. Parameshwaran et al. 2014) [32].
The review of literature does reveal that there haven’t been any comprehensive
study regarding employee evaluation as well as organizational growth due to better
practice of employee appraisal system. This paper contemplates to propose a
direction in the view of sheading some light in this research gap by implementing
66
Haq & Ahmed
Fuzzy TOPSIS methodology which solves a scenario of employee evaluation in a
reputed manufacturing company in Bangladesh based on critical criteria which have
their own importance determined by the decision maker to order the employees in
consideration from best to worst.
3. Fuzzy TOPSIS Methodology
Extension of TOPSIS to fuzzy environment was done by C.-T. Chen (2000) [33],
substituted directly provided crisp data with fuzzy linguistic value for making grade
assessment. The modification in this algorithm helps to match that of a thinking of
human in a realistic environment (A. Yeşim Yayla 2012) [34]. The fuzzy theory
provides linguistic expressions which are considered preferences/judgments of an
individual.
In the fuzzy TOPSIS procedure, the fuzzy importance weights of the criteria
,.....,2,1;
~
(=jWj
number of criteria (n)) and the fuzzy rating of alternatives at
criteria
,.....,2,1;
~
(=iXIj
number of alternative (m)
,.....,2,1=j
number of criteria
(n)) are inputs that are placed in a matrix. The fuzzy TOPSIS procedure consists of
the following steps (A. Yeşim Yayla 2012):
Step 3.1: Inputs are expressed in the decision matrix as:
mnmml
nl
l
xxx
xxx
xxx
D
~~~
~~~
~~~
~
2
2222
ln121
=
(1)
n
wwwwW ~
.....
~~~
~321 +++=
(2)
Step 3.2: Calculate the normalized fuzzy decision matrix:
max
~
~
ij
rR =
;
,.....,2,1=i
number of alternative (m)
,.....,2,1=j
number of criteria
(n)). Where for benefit criteria,
=+++
j
ij
j
ij
j
ij
ij u
u
u
m
u
l
r,,
~
(3)
Where,
+
j
u
= max
ij
u
(4)
For cost criteria,
=
−−−
ij
j
ij
j
ij
j
ij u
l
u
l
u
l
r,,
~
(5)
Where,
−
j
i
= min
ij
i
(6)
Step 3.3: Calculate the weighted normalized fuzzy decision matrix,
V
~
:
67
A comprehensive study of Fuzzy TOPSIS ....
nm
ij
vV
=~
~
(7)
jijij wrv ~~~ =
(8)
Where
ij
v
~
is the fuzzy weight of
jth
criterion.
Step 3.4: Identify the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal
solution (FNIS)
++++ =n
vvvS ~
,.......,
~
,
~21
(9)
−−−− =n
vvvS ~
,.......,
~
,
~21
(10)
Where
( )
0,0,0
~=
+
j
v
&
( )
0,0,0
~=
−
j
v
Step 3.5: Calculate the distances of each alternative to the fuzzy positive ideal
solution and fuzzy negative ideal solution using
( )
=
++ −= n
jjijivvdd
1
~~
(11)
( )
=
−+ −= n
jjijivvdd
1
~~
(12)
For triangular fuzzy numbers the equation is expressed as:
( )
( ) ( ) ( )
2
21
2
21
2
21
3
1
~
,
~uummllBAd −+−+−=
(13)
Step 3.6: Compute the relative closeness of alternative
−+
−
+
=
ii
i
idd
d
C
(14)
Where, 0 ≤
i
C
≤ 1 that is, alternative i is closer to the fuzzy positive ideal reference
point and far from the fuzzy negative ideal reference point as Ci approaches.
Step 3.7: Rank the preference order. Choose the alternative with maximum
i
C
value.
4. Fuzzy TOPSIS Application
In this research, triangular fuzzy numbers have been implemented for evaluating
criteria weights and alternative ratings. The weightages based on importance of
various criteria and the ratings of qualitative criteria are contemplated as linguistic
variables. These importance weights, linguistic variables and ratings, have been
68
Haq & Ahmed
asserted in positive triangular fuzzy numbers as shown in Tables 1. The weights of
employees’ performances evaluation criteria and evaluation ratings of employees’
performances evaluation given in Table 1 are quantified by using linguistic values.
Three top management managers have weighted fourteen decision criteria based on
the linguistic variables in Table 1. Also, performance evaluation of personnel is
performed by production floor supervisors, managers and external executives based
on the linguistic variables in Table 1. The assessments carried out by using
linguistic variables are given as a membership function by transforming fuzzy
triangular numbers. For instance, if some manager evaluates any decision criterion
as ‘very high’, the membership function is defined as (0.9,1,1) and it is transformed
into a fuzzy triangular number. The decision makers use the linguistic weighting
variables as shown in Table 1 to assess the importance of the criteria and then
fourteen decision criteria were evaluated by three managers and are presented in
Table 3. The performance of employees are evaluated by production floor
supervisors, managers and external executives based on the qualitative attributes
(criteria) and reached the production floor performance which have been shown in
Table 4. This condition is the same as the performance of production floor.
Table 1. Linguistic variables for weight of each criterion at the left (used by
managers of production floor). Linguistic variables for the ratings at the
right (used by managers, supervisors of production floor and external
executives)
Linguistic Variables
Triangular fuzzy
numbers (TFNs)
Very high (VH)
(0.9, 1, 1)
High (H)
(0.7, 0.9, 1)
Medium high (MH)
(0.5, 0.7, 0.9)
Medium (M)
(0.3, 0.5, 0.7)
Medium low (ML)
(0.1, 0.3, 0.5)
Low (L)
(0, 0.1, 0.3)
Very low (VL)
(0, 0, 0.1)
Linguistic Variables
Triangular fuzzy
numbers (TFNs)
Very good (VG)
(9, 10, 10)
Good (G)
(7, 9, 10)
Medium good (MG)
(5, 7, 9)
Fair (F)
(3, 5, 7)
Medium poor (MP)
(1, 3, 5)
Poor (P)
(0, 1, 3)
Very poor(VP)
(0, 0, 1)
69
A comprehensive study of Fuzzy TOPSIS ....
Table 2. Decision matrix using fuzzy linguistic variables
Criteria
Importance
DM-1
DM-2
DM-3
C1
Job Capability and Knowledge
VH
H
MH
C2
Prompt Management of Time and Schedule
H
VH
H
C3
Machine and Equipment Maintainability
H
MH
ML
C4
Job efficiency and Perception
VH
H
H
C5
Management of Organizational Hierarchy
MH
MH
H
C6
Professionalism in Attitude
ML
MH
M
C7
Planning and Leadership capability
M
H
MH
C8
Ability to Self-educate and Self-development
VH
H
H
C9
Communication skill and team work
M
MH
MH
C10
Absenteeism
ML
L
M
C11
Dependability and Adopting pressure
H
MH
ML
C12
Job integrity and Work ethics
MH
MH
M
C13
Innovation and Intuitiveness
M
ML
MH
C14
Appearance and Outlook
VH
H
VH
Table 3. Fuzzy attribute weights for crucial criteria
Criteria
Weights
C1
Job Capability and Knowledge
0.700, 0.867, 0.967
C2
Prompt Management of Time and Schedule
0.767, 0.933, 1.000
C3
Machine and Equipment Maintainability
0.433, 0.633, 0.800
C4
Job efficiency and Perception
0.767, 0.933, 1.000
C5
Management of Organizational Hierarchy
0.567, 0.767, 0.933
C6
Professionalism in Attitude
0.300, 0.500, 0.700
C7
Planning and Leadership capability
0.500, 0.700, 0.867
C8
Ability to Self-educate and Self-development
0.767, 0.933, 1.000
C9
Communication skill and team work
0.433, 0.633, 0.833
C10
Appearance and Outlook
0.133, 0.300, 0.500
C11
Dependability and Adopting pressure
0.433, 0.633, 0.800
C12
Job integrity and Work ethics
0.433, 0.633, 0.833
C13
Innovation and Intuitiveness
0.300, 0.500, 0.700
C14
Absenteeism
0.833, 0.967, 1.000
70
Haq & Ahmed
Table 4. The performance ratings of employees evaluated by production floor supervisors, managers and external executives based
on the qualitative attributes
Criteria
Employee
Decision Makers
Criteria
Employee
Decision Makers
Production floor
Supervisors
Managers
External Executives
Production
floor
Supervisors
Managers
External
Executives
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
Job Capability
and
Knowledge
E1
7
9
10
5
7
9
3
5
7
Ability to
Self-educate
and Self-
development
E1
5
7
9
5
7
9
5
7
9
E2
5
7
9
5
7
9
3
5
7
E2
7
9
10
5
7
9
3
5
7
E3
7
9
10
7
9
10
7
9
10
E3
5
7
9
7
9
10
7
9
10
E4
7
9
10
5
7
9
7
9
10
E4
1
3
5
0
1
3
1
3
5
E5
9
10
10
7
9
10
7
9
10
E5
5
7
9
3
5
7
5
7
9
Prompt
Management
of Time and
Schedule
E1
5
7
9
7
9
10
7
9
10
Communication
skill and team
work
E1
3
5
7
3
5
7
1
3
5
E2
5
7
9
1
3
5
5
7
9
E2
1
3
5
0
0
1
0
1
3
E3
7
9
10
9
10
10
5
7
9
E3
5
7
9
7
9
10
7
9
10
E4
3
5
7
7
9
10
7
9
10
E4
3
5
7
5
7
9
3
5
7
E5
7
9
10
7
9
10
5
7
9
E5
9
10
10
7
9
10
9
10
10
Machine and
Equipment
Maintainability
E1
7
9
10
3
5
7
3
5
7
Appearance
and Outlook
E1
3
5
7
3
5
7
3
5
7
E2
7
9
10
3
5
7
5
7
9
E2
7
9
10
5
7
9
7
9
10
E3
5
7
9
5
7
9
3
5
7
E3
5
7
9
7
9
10
5
7
9
E4
7
9
10
1
3
5
3
5
7
E4
1
3
5
1
3
5
0
1
3
E5
9
10
10
7
9
10
5
7
9
E5
9
10
10
7
9
10
5
7
9
Job efficiency
and
Perception
E1
7
9
10
5
7
9
5
7
9
Dependability
and Adopting
pressure
E1
7
9
10
5
7
9
5
7
9
E2
5
7
9
3
5
7
3
5
7
E2
5
7
9
7
9
10
3
5
7
E3
9
10
10
5
7
9
7
9
10
E3
9
10
10
7
9
10
7
9
10
E4
7
9
10
7
9
10
5
7
9
E4
1
3
5
0
1
3
1
3
5
E5
5
7
9
7
9
10
7
9
10
E5
7
9
10
7
9
10
7
9
10
Management
of
Organizational
Hierarchy
E1
7
9
10
7
9
10
7
9
10
Job integrity
and Work
ethics
E1
7
9
10
3
5
7
3
5
7
E2
3
5
7
5
7
9
1
3
5
E2
5
7
9
3
5
7
7
9
10
E3
7
9
10
9
10
10
7
9
10
E3
7
9
10
7
9
10
5
7
9
E4
5
7
9
7
9
10
3
5
7
E4
0
1
3
0
1
3
0
1
3
E5
7
9
10
7
9
10
7
9
10
E5
9
10
10
7
9
10
7
9
10
Professionalism
in Attitude
E1
5
7
9
1
3
5
0
1
3
Innovation
and
Intuitiveness
E1
3
5
7
3
5
7
3
5
7
E2
0
1
3
1
3
5
0
1
3
E2
3
5
7
1
3
5
1
3
5
E3
7
9
10
5
7
9
1
3
5
E3
9
10
10
7
9
10
9
10
10
E4
3
5
7
1
3
5
0
1
3
E4
5
7
9
7
9
10
7
9
10
E5
9
10
10
3
5
7
5
7
9
E5
7
9
10
3
5
7
3
5
7
Planning and
Leadership
capability
E1
0
1
3
1
3
5
3
5
7
Absenteeism
E1
0
1
3
3
5
7
1
3
5
E2
5
7
9
3
5
7
3
5
7
E2
1
3
5
1
3
5
0
1
3
E3
9
10
10
7
9
10
5
7
9
E3
9
10
10
7
9
10
7
9
10
E4
1
3
5
5
7
9
0
1
3
E4
5
7
9
7
9
10
9
10
10
E5
9
10
10
7
9
10
7
9
10
E5
7
9
10
9
10
10
9
10
10
71
A comprehensive study of Fuzzy TOPSIS ....
Table 5. Fuzzy numbers of the aggregated ratings of the employees evaluated by managers, production floor supervisors and external
executives.
Em.
Criteria
C1
C2
C3
C4
C5
C6
C7
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
E1
5.00
7.00
8.67
6.33
8.33
9.67
4.33
6.33
8.00
5.67
7.67
9.33
7.00
9.00
10.00
2.00
3.67
5.67
1.33
3.00
5.00
E2
4.33
6.33
8.33
3.67
5.67
7.67
5.00
7.00
8.67
3.67
5.67
7.67
3.00
5.00
7.00
0.33
1.67
3.67
3.67
5.67
7.67
E3
7.00
9.00
10.00
7.00
8.67
9.67
4.33
6.33
8.33
7.00
8.67
9.67
7.67
9.33
10.00
4.33
6.33
8.00
7.00
8.67
9.67
E4
6.33
8.33
9.67
5.67
7.67
9.00
3.67
5.67
7.33
6.33
8.33
9.67
5.00
7.00
8.67
1.33
3.00
5.00
2.00
3.67
5.67
E5
7.67
9.33
10.00
6.33
8.33
9.67
7.00
8.67
9.67
6.33
8.33
9.67
7.00
9.00
10.00
5.67
7.33
8.67
7.67
9.33
10.00
Criteria
C8
C9
C10
C11
C12
C13
C14
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
E1
5.00
7.00
9.00
2.33
4.33
6.33
3.00
5.00
7.00
5.67
7.67
9.33
4.33
6.33
8.00
3.00
5.00
7.00
1.33
3.00
5.00
E2
5.00
7.00
8.67
0.33
1.33
3.00
6.33
8.33
9.67
5.00
7.00
8.67
5.00
7.00
8.67
1.67
3.67
5.67
0.67
2.33
4.33
E3
6.33
8.33
9.67
6.33
8.33
9.67
5.67
7.67
9.33
7.67
9.33
10.00
6.33
8.33
9.67
8.33
9.67
10.00
7.67
9.33
10.00
E4
0.67
2.33
4.33
3.67
5.67
7.67
0.67
2.33
4.33
0.67
2.33
4.33
0.00
1.00
3.00
6.33
8.33
9.67
7.00
8.67
9.67
E5
4.33
6.33
8.33
8.33
9.67
10.00
7.00
8.67
9.67
7.00
9.00
10.00
7.67
9.33
10.00
4.33
6.33
8.00
8.33
9.67
10.00
Table 6. Weighted normalized fuzzy decision matrix
Em.
Criteria
C1
C2
C3
C4
C5
C6
C7
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
E1
0.350
0.61
0.84
0.50
0.80
1.00
0.19
0.41
0.66
0.45
0.74
0.97
0.40
0.69
0.93
0.07
0.21
0.46
0.07
0.21
0.43
E2
0.303
0.55
0.81
0.29
0.55
0.79
0.22
0.46
0.72
0.29
0.55
0.79
0.17
0.38
0.65
0.01
0.10
0.30
0.18
0.40
0.66
E3
0.490
0.78
0.97
0.56
0.84
1.00
0.19
0.41
0.69
0.56
0.84
1.00
0.43
0.72
0.93
0.15
0.37
0.65
0.35
0.61
0.84
E4
0.443
0.72
0.93
0.45
0.74
0.93
0.16
0.37
0.61
0.50
0.80
1.00
0.28
0.54
0.81
0.05
0.17
0.40
0.10
0.26
0.49
E5
0.537
0.81
0.97
0.50
0.80
1.00
0.31
0.57
0.80
0.50
0.80
1.00
0.40
0.69
0.93
0.20
0.42
0.70
0.38
0.65
0.87
Criteria
C8
C9
C10
C11
C12
C13
C14
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
E1
0.397
0.676
0.931
0.101
0.274
0.528
0.041
0.155
0.362
0.246
0.486
0.747
0.188
0.401
0.667
0.090
0.250
0.490
0.111
0.215
0.500
E2
0.397
0.676
0.897
0.014
0.084
0.250
0.087
0.259
0.500
0.217
0.443
0.693
0.217
0.443
0.722
0.050
0.183
0.397
0.128
0.276
1.000
E3
0.502
0.805
1.000
0.274
0.528
0.806
0.078
0.238
0.483
0.332
0.591
0.800
0.274
0.528
0.806
0.250
0.483
0.700
0.056
0.069
0.087
E4
0.053
0.225
0.448
0.159
0.359
0.639
0.009
0.072
0.224
0.029
0.148
0.347
0.000
0.063
0.250
0.190
0.417
0.677
0.057
0.074
0.095
E5
0.344
0.611
0.862
0.361
0.612
0.833
0.097
0.269
0.500
0.303
0.570
0.800
0.332
0.591
0.833
0.130
0.317
0.560
0.056
0.067
0.080
72
Haq & Ahmed
Table 7. The fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS)
Criteria
C1
C2
C3
C4
C5
C6
C7
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
FPIS, A+
0.537
0.809
0.967
0.555
0.837
1.000
0.314
0.568
0.800
0.555
0.837
1.000
0.434
0.716
0.933
0.196
0.423
0.700
0.383
0.653
0.867
FNIS, A-
0.303
0.549
0.806
0.291
0.547
0.793
0.164
0.371
0.607
0.291
0.547
0.793
0.170
0.383
0.653
0.012
0.096
0.296
0.067
0.210
0.433
Criteria
C8
C9
C10
C11
C12
C13
C14
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
l
m
u
FPIS, A+
0.502
0.805
1.000
0.361
0.612
0.833
0.097
0.269
0.500
0.332
0.591
0.800
0.332
0.591
0.833
0.250
0.483
0.700
0.128
0.276
1.000
FNIS, A-
0.053
0.225
0.448
0.014
0.084
0.250
0.009
0.072
0.224
0.029
0.148
0.347
0.000
0.063
0.250
0.050
0.183
0.397
0.056
0.067
0.080
Table 8. Distances of the ratings of each alternative from S+ and S- with respect to each criterion
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
di+
D(E1, S+)
0.175
0.036
0.137
0.085
0.026
0.200
0.402
0.104
0.303
0.108
0.085
0.168
0.203
0.291
2.324
D(E2, S+)
0.222
0.256
0.095
0.256
0.294
0.318
0.221
0.113
0.496
0.008
0.125
0.126
0.272
0.000
2.802
D(E3, S+)
0.032
0.000
0.129
0.000
0.000
0.053
0.037
0.000
0.072
0.023
0.000
0.052
0.000
0.542
0.939
D(E4, S+)
0.076
0.092
0.181
0.036
0.153
0.240
0.355
0.530
0.218
0.202
0.406
0.493
0.054
0.537
3.572
D(E5, S+)
0.000
0.036
0.000
0.036
0.026
0.000
0.000
0.165
0.000
0.000
0.021
0.000
0.144
0.546
0.973
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
di-
D(E1, S-)
0.047
0.226
0.044
0.175
0.273
0.119
0.000
0.430
0.201
0.095
0.327
0.328
0.070
0.259
2.595
D(E2, S-)
0.000
0.000
0.088
0.000
0.000
0.000
0.184
0.417
0.000
0.197
0.284
0.372
0.000
0.546
2.090
D(E3, S-)
0.195
0.256
0.057
0.256
0.294
0.267
0.366
0.530
0.437
0.182
0.406
0.447
0.272
0.004
3.968
D(E4, S-)
0.149
0.165
0.000
0.226
0.142
0.079
0.047
0.000
0.287
0.000
0.000
0.000
0.225
0.010
1.330
D(E5, S-)
0.222
0.226
0.181
0.226
0.273
0.318
0.402
0.367
0.496
0.202
0.391
0.493
0.130
0.000
3.929
73
A comprehensive study of Fuzzy TOPSIS ....
Table 9. Ranking of employee's according to Fuzzy TOPSIS
Employee
CCi
Rank
E1
0.527558332
3
E2
0.427191717
4
E3
0.808574897
1
E4
0.271396619
5
E5
0.801505969
2
Fuzzy numbers of the aggregated ratings of the employees evaluated by managers,
production floor supervisors and external executives are provided in table 5. After
which, normalized fuzzy decision matrix is created by applying equation-3 and
equation-5 respectively for beneficial and cost criteria. From which weighted
normalized fuzzy decision matrix is produced using equation-8 which is shown in
Table 6. The fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution
(FNIS) is then identified using equation-11 and equation-12 respectively. Distances
of the ratings of each alternative from S+ and S- with respect to each criterion is
calculated using equation -13. And finally, the relative closeness of alternatives
were determined which provided the ranking of employee's according to Fuzzy
TOPSIS which is as follows-
E3 > E5 > E1 > E2 > E4
5. Conclusion
This study suggests a simple and easy-to-use MCDM approach to evaluate
employee performances for the need of organizational behavior development.
Based on the literature survey and with the validation of industrial experts, possible
employee performance evaluation criteria were defined. The fuzzy TOPSIS
approaches used in this study offered a more precise and accurate analysis by
integrating interdependent relationships within and among a set of criteria. The
intuitionistic fuzzy TOPSIS method is a suitable method for MCDM because it
contains a vague perception of decision makers’ opinions. Moreover, fuzzy
TOPSIS method helps to choose the alternative for ideal solution of this problem
efficiently. In this research, fourteen input variables for five employees are
considered to determine the best employee. Some other input variables may also be
considered to find the result which depends on the purpose of the evaluation system
of company. Results presented in the proposed fuzzy MCDM method is practical
74
Haq & Ahmed
and useful. Other possible techniques that might be employed for future research
include VIKOR and PROMETHEE; results obtained from these methods could be
compared with the results obtained from this work.
References
[1]
Meredith, J.R., (1992)
, “The management of operations: a conceptual
emphasis”, 4th ed. New York: John
Wiley & Sons.
[2]
Vonderembse, M.A. and White, G.P., (1995)
, “Operations
management concepts, methods and strategies” 2nd ed. New York: West
Publishing Company.
[3]
Chase, R.B. and Aquilano, N.J., (1992)
, “Production and operations
management: a life cycle approach” New York: McGraw-Hill.
[4] Neely, A.D., Gregory, M., and Platts, K., (1995), “Performance
measurement system design”, International Journal of Operations and
Production Management, Vol. 15, No. 4, pp 80–116.
[5]
A
mmons, D.N., (1996)
, “Municipal benchmarks: assessing local
performance and establishing community standards”, Thousand Oaks,
CA: Sage Publications.
[6]
Berman, E.M., (1998)
, “Productivity in public and non-profit
organizations: strategies and techniques”, Thousand Oaks, CA: Sage
Publications.
[7]
Hershey, P. and Blanchard, K.H., (1969)
, “Life cycle theory of
leadership: Is there a best style of leadership?”, Training and
Development Journal, Vol. 33, No. 6, pp 26–34.
[8]
Sahay, B.S., (2005)
, “Multi-factor productivity measurement model for
service organization”, International Journal of Productivity and
Performance Management, Vol. 54, No. 1, pp 7–22.
[9]
Triantaphyllou, E., (2000)
, “Multi-criteria decision-making methods:
a comparative study (applied optimization”, Dortrecht, NL: Kluwer
Academic Publishers, Vol. 44.
[10] Hwang, C.L. and Yoon, K. (1981), “Multiple attribute decision making”,
Berlin: Springer-Verlag.
75
A comprehensive study of Fuzzy TOPSIS ....
[11]
McLaughlin, C.P. and Coffey, S., (1990)
, “Measuring productivity in
services”, International Journal of Service Industry Management, Vol.
1, No. 1, pp 46–64.
[12]
Ghalayani, A. M. and Noble, S. J., (1996)
, “The changing basis of
performance measurement”, International Journal of Operations and
Production Management, Vol. 16, No. 8, pp 63–80.
[13]
Gomes, C.F., Yasin, M.M., and Lisboa, J.V., (2004)
, “A literature
review of manufacturing performance measures and measurement in an
organizational context: a framework and direction for future research”,
Journal of Manufacturing Technology Management, Vol. 15, No. 6, pp
511–530.
[14]
Simar, L. and Wilson, P.W., (2008)
, “Statistical inference in
nonparametric frontier models: recent developments and perspectives,
In: H.O. Fried, C.A.K. Lovell and S.S. Schmidt, eds”, The measurement
of productive efficiency and productivity growth. Oxford: Oxford
University Press, pp 421–522.
[15] Kilduff, M., Angelmar, R. and Mehra, A. (2000), “Top management team
diversity and firm performance: examining the role of cognitions”,
Organization Science, Vol. 11, No. 1, pp. 21-34.
[16] Higgs, M. (2005), “Inuence of team composition and task complexity on
team performance”, Team Performance Management, Vol. 11, Nos 7/8, pp.
227-250.
[17] Ying-Feng, K. and Ling-Show, C. (2002), “Using the fuzzy synthetic
decision approach to assess the performance of university teachers in
Taiwan”, International Journal of Management, Vol. 19, No. 4, pp. 593-
604.
[18] Kciuk, M. (2007), “Personnel management in the aspect of company
management”, Journal of Achievements in Material and Manufacturing
Engineering, Vol. 25, No. 2, pp. 91-94.
[19] Wua, H.-Y., Tezng, G.-H. and Chen., Y.-H. (2009), “A fuzzy MCDM
approach for evaluating banking performance based on balanced
scorecard”, Expert Systems with Applications, Vol. 36, No. 6, pp. 10135-
10147.
76
Haq & Ahmed
[20] Sun, C.-C. (2010), “A performance evaluation model by integrating fuzzy
AHP and fuzzy TOPSIS methods”, Expert Systems with Applications, Vol.
37, No. 12, pp. 7745-7754.
[21] Parkan, C. and Wu, M. (1999), “Decision-making and performance
measurement models with applications to robot selection”, Computers and
Industrial Engineering, Vol. 36, No. 3, pp 503–523.
[22] Deng, H., Yeh, C. and Willis, R.J. (2000), “Inter-company comparison
using modified TOPSIS with objective weights”, Computers and
Operations Research, Vol. 27, No. 10, pp 963–973.
[23] Jee, D. and Kang, K. (2000), “A method for optimal material selection
aided with decision making theory”, Materials and Design, Vol. 21, No. 3,
pp 199–206.
[24] Wang, B.H., et al. (2007), “Research on FTOPSIS model of threat
synthetic evaluation in multi-target tracing system”, In: Proceedings of
2007 IEEE international conference on industrial engineering and
engineering management, 2–4 December Singapore, pp 35–39.
[25] Wu H.Y., Tzeng G.H. and Chen Y.H (2009), “A fuzzy MCDM approach
for evaluating banking performance based on Balanced Scorecard”, Expert
Systems with Applications, Vol. 36, pp 10135–10147.
[26] Kaya T., Kahraman C. (2011), “Fuzzy multiple criteria forestry decision
making based on an integrated VIKOR and AHP approach”, Expert
Systems with Applications, Vol. 38, pp 7326–7333.
[27] Deng, Y., Chan, F. T. S., Wu, Y. and Wang, D. (2011), “A new linguistic
MCDM method based on multiple-criterion data fusion,” Expert Systems
with Applications, Vol. 38, No. 6, pp. 6985–6993.
[28] Alam, M. N. E., Lipi, T. F., Hasin, M. A. A. and Ullah, A. M. M. S.
(2011), “Algorithms for fuzzy multi expert multi criteria decision making
(ME-MCDM),” Knowledge-Based Systems, Vol. 24, No. 3, pp. 367–377.
[29] Opricovic S. and Tzeng, G.-H. (2004), “Compromise solution by MCDM
methods: a comparative analysis of VIKOR and TOPSIS,” European
Journal of Operational Research, Vol. 156, No. 2, pp. 445–455.
77
A comprehensive study of Fuzzy TOPSIS ....
[30] Saaty, T. L. (2006), “Fundamentals of Decision Making and Priority
Theory with the Analytic Hierarchy Process”, RWS Publications,
Pittsburgh, Pa, USA.
[31] Lin, H.-T. (2010), “Personnel selection using analytic network process and
fuzzy data envelopment analysis approaches,” Computers and Industrial
Engineering, Vol. 59, No. 4, pp. 937–944.
[32] Parameshwaran, R., Praveen Kumar, S. and Saravanakumar, K.
(2014), “An integrated fuzzy MCDM based approach for robot selection
considering objective and subjective criteria,” Applied Soft Computing
Journal, Vol. 26, pp. 31–41.
[33] Chen, C.-T. (2000), “Extensions of the TOPSIS for group decision-making
under fuzzy environment”, Fuzzy Sets Systems, Vol. 114, No. 1, pp 1–9.
[34] Yayla, A. Y., Yildiz, A. and Ozbek, A. (2012), ‘’Fuzzy TOPSIS method in
supplier selection and application in the garment industry”, Fibres Text.
East. Eur., Vol. 93, No. 4, pp 20–23.
