#_05_Snezana Knezevic:tipska.qxd

Snežana Knežević1, Ksenija Mandić1,Aleksandra Mitrović2, Veljko Dmitrović1, Boris Delibašić1
1University of Belgrade, Faculty of Organizational Sciences, Serbia

2University of Kragujevac, Faculty of Hotel Management and Tourism, Serbia

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

UDC:

An FAHP-TOPSIS Framework for Analysis of
the Employee Productivity in the Serbian
Electrical Power Companies
DOI: 10.7595/management.fon.2017.0011

1. Introduction

Continuous technological progress puts more complex demands before company employees. In this con-
text, the management of the company is expected to activate all relevant components through appropriate
organisational structures to increase the productivity of employees.

Employees can create added value, and this stems from a combination of factors of the situation and char-
acteristics of workers, primarily of a manager, who represents the driving force of the company. Stewart
(1991) defined intellectual capital (IC) as “knowledge, information, intellectual property, experience – that can
be put to use to create wealth”. Roos et al. (2005) classify intellectual capital into human capital, organisa-
tional capital, and relational capital. According to Peng et al. (2007), “intellectual capital is the set of critical
resources used by firms to facilitate productive activities and generate economic rents”. Employees repre-
sent the intellectual equity of the company if they have a sufficient amount of formal education, experience
and ability, learned reflex or even talent to react in a crisis and expected situations in order to make more

Abstract: The aim of this paper is to apply an integrated model, which combines methods of classical and
fuzzy Multi-criteria decision making (MCDM) in selected six large equity companies from the Serbian energy
sector. The data considered are retrieved from the official financial statements. Four main criteria were ana-
lyzed, identified by the previous researchers and pointing to the employees’ productivity: Operating in-
come/Number of employees, Equity/Number of employees, Net income/Number of employees and Total
assets/Number of employees. The contribution of this paper lies in the application of a hybrid model that in-
tegrates two MCDM methods: Fuzzy Analytic Hierarchy Process (FAHP) and Technique for Order Perform-
ance by Similarity to Ideal Solution (TOPSIS) to analyse the employee productivity in selected D-Electrical
power supply companies operating in Serbia. The FAHP is an effective method for mathematical representa-
tion of uncertain and imprecise evaluations made by humans, while the TOPSIS method is an efficient way to
rank the alternatives. Results show that operating income is of highest importance for estimating employee pro-
ductivity and decision making, while equity is of the weakest. Furthermore, the most productive operations in
large enterprises from selected companies of the sector D-Electrical power supply are found in the company
PC EPS Beograd, and the lowest are in the ED Center llc Kragujevac.

Keywords: employee productivity, Serbian companies, electricity sector, fuzzy logic, MCDM methods, FAHP,
TOPSIS.

JEL classification: C20, C60, P28, Q40, J24

Corresponding author: Snezana Knezevic, e-mail: knezevic.snezana@fon.bg.ac.rs

accurate business decisions (Lentjusenkova & Lapina 2016). This equity merges into the enterprise and
creates value thereof. The efficiency of the company is an expression of performance adjustment to market
environment and internal operating conditions, which is necessary for the survival, growth and develop-
ment. The efficiency of enterprises is a synthetic indicator of the output to input relation, i.e., it demonstrates
the successfulness of a company in the use of resources at its disposal - material and human resources. In
this context, it is especially important nowadays that companies develop a mechanism for proper manage-
ment of the employee productivity. Also necessary for this is an appropriate reporting system, both at the
enterprise level and at the narrower organisational department one, as well as a strong support of informa-
tion technology.

According to classical economic theory, efficiency is measured as the ratio between one output and one
input. However, in practice, this is much more complex as the entities have many different inputs and out-
puts. The problem arises if you cannot find a common term for them. Generally speaking, the principle of
efficiency is achieved if there are the highest possible economic effects of output values (output) with min-
imum economic investment (input). It should especially be borne in mind that in times of economic crises,
each company must perceive competitors in order to improve the efficiency of operations.

Efficiency is measured as the ratio between one output and one input and companies have many diverse
inputs and outputs (Markovic et al., 2015). Productivity is an important instrument for increasing the overall
efficiency of banks (Andries, 2011) and insurance companies. To manage the productivity of employees in
enterprises, it is possible to use different ratios, as follows (Knezevic, 2006):

• Operating income/Total number of employees in the company;

• Operating income/Number of full time employees in the company;

• Operating income/Total number of effective work hours;

• Net income/Total number of employees in the company;

• Net income/Number of full time employees in the company;

• Equity/Total number of employees in the company;

• Equity/Total number of full time employees in the company;

• Net profit/Number of organisational units of the company;

• Net income/Total number of effective working hours;

• Profit centre income/Total number of employees in the profit center;

• Profit centre income/Total number of full time employees in the profit center;

• Profit centre income/Total number of effective working hours, as well as many other indicators.

“Efficiency shows the degree of effectiveness of the companies that have specific inputs (equity and re-
serves, deposits, borrowings, engaged funds, property) for the production or services to obtain the output
values, e.g., revenues and profit” (Knezevic et al., 2015). Equity and Total assets are the key inputs pre-
sented in the balance sheet. Operating income and Net income are the key financial outputs presented in
the income statement. Inputs and outputs are correlated. As a base for research in this paper four coefficients
were used to test the productivity of employees, as follows: 1) Operating income/Number of employees, 2)
Equity/Number of employees, 3) Net income/Number of employees and 4) Total assets/Number of em-
ployees. The number of workers can be expressed in two ways, that is, as the strength of the workers who
are on the job and as the average number of employees based on working hours.

The study includes the sample of six companies among the largest first-ranked by the equity in Serbia. The
criteria for selection was the high degree of concentration of financial power for companies operating in the
same sector (electricity power supply, six top-ranked) and which are classified as large companies. For the
selected companies, public accessible, relevant financial information and data were taken from the Agency
for Business Registers. There are financial reports of companies published, as well as statistics on the num-
ber of employees from the same source (http://www.apr.gov.rs/, 2017).

The starting hypothesis of the research is: The use of linguistic variables, which are expressed by triangu-
lar fuzzy numbers, allows decision-makers to calculate more realistic weights of criteria and thus enable
more effective ranking of alternatives. The aim of this research is to analyse the employee productivity in se-

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

lected Serbian electrical power companies by using FAHP-TOPSIS model. Within the paper, an integrated
model for ranking the companies from the sector of the D-electrical power supply is proposed by four co-
efficients of employee productivity. This model combines the method of fuzzy MCDM such as FAHP and the
method of classical MCDM such as TOPSIS. The objective of this paper is to determine the priority weights
for four primary coefficients of employee productivity using FAHP method; while using the TOPSIS method
ranking of the companies from the sector of the D-electrical power supply is performed on the basis of the
mentioned coefficients. It is of practical interest to explore how classical and fuzzy MCDM methods can be
combined and the manner in which they contribute to the process of ranking. The priority vectors for the se-
lected criteria are set by including the fuzzy MCDM (FAHP) method in the research. This method involves
the use of fuzzy numbers and thus does not require precise (numerically determined) information. By using
this method, it is possible to work with uncertain and imprecise data. On the other hand, using the classical
MCDM method, TOPSIS enabled the ranking of companies and in this way it is possible to determine which
company is closer to the Positive Ideal Solution or farther to the Negative Ideal Solution.

The paper is structured as follows. Section 2 presents a brief literature overview about productivity and
application of the different models. Section 3 points to the used sample and methodology. However, the
appendix covers a brief outline of the used FAHP and TOPSIS methods. Besides, a used model con-
structed by integrating the presented MCDM methods is also presented. The proposed model allows the
ranking of large companies from the sector of D-electrical power supply concerning the productivity of em-
ployees. Section 4 presents findings, results and discussion. The paper ends with concluding remarks in
Section 5.

2. Literature overview

Economic engagement of the factors of production in the field of production of goods and generating serv-
ices where sales price exceeds the costs is more and more in the focus of new entrepreneurship due to in-
creasingly complex operating conditions and tough competition in the market. In this framework, there is a
close connection between economics and management in the company and the way their relationship de-
termines their effectiveness and efficiency at the company level. Indicators focused on the relationship be-
tween a company’s input and output elements are productivity, efficiency and profitability. In the economic
theory discussed and in the economic practices implemented there are various quantitative (and qualitative)
sets of indicators.

Productivity should be monitored in relation to the planned size or realisation of similar size (comparable)
companies, but the comparison with the leader in the relevant branch should also be monitored. According
to Knezevic et al. (2012), productivity can be measured as a quotient of one output and one input; then the
obtained indices are divided from one period to another. One of the plans of strategic importance for the
company is the plan of measures to increase the company’s productivity.

According to Knezevic (2006), factors of labour productivity in enterprises can in principle be systematised
in two parts, objective factors and subjective factors) or in three parts:

(1) absolutely objective factors - general economic conditions (the pace of development of science
and technology, market development);

(2) relatively objective factors - specific economic conditions in the market (location and capacity of
the company, financial strength and business orientation, technology, organisation) and

(3) subjective factors of company - specific activities – managing company, motivating employees,
staff attitudes, working conditions and employees’ living conditions).

Economic efficiency and an increase of labour productivity are of particular interest due to their importance
for progress in any field and level. Based on particular research interests issue of productivity can be
analysed. There are productivity differences due to many factors (Syverson, 2011). In recent years, inno-
vation and new technologies are seen as factors that have a significant influence on productivity and or-
ganisational performances (Skare and Tomic, 2016).There are several methods and models which are
used for measuring productivity and efficiency of decision-making units. The most popular methods of
evaluation and benchmarking for performances of decision-making units are Data Envelopment Analysis
(DEA), Stochastic Frontier Analysis and Distance Based Analysis (DBA) (Çelen, 2013; Jayaraman et al.,

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

2013). Many factors can have an impact on the efficiency and productivity but also can be mutually con-
flicted. Due to this fact, multiple-criteria decision-making (MCDM) is necessary to be implemented. In the
literature a multitude of papers can be found that have developed models based on the MCDM methods.
In most of the papers, in addition to the classic MCMD method, also used is the theory of fuzzy sets, as
an effective way to mathematically represent vague and imprecise human preferences. In recent years,
numerous authors applied classical MCDM method in combination with fuzzy methods for choosing the
optimal solution: Patil & Kant (2014) created a fuzzy AHP-TOPSIS framework for ranking the solutions of
knowledge management adoption in the supply chain to overcome its barriers. On the other hand, Prakash
& Barua (2015) integrated AHP-TOPSIS method for prioritising the solutions of reverse logistics adoption
to overcome its barriers under fuzzy environment. Also, Zyoud et al. (2016) proposed the integrated FAHP-
FTOPSIS model for dealing with complicated issues in the context of water loss management. Hosseini
& Keshavarz (2017) used FAHP and FTOPSIS for strategic analysis measurement of service quality in the
banking industry. To analyse the e-service quality of banking internet Özdaðoðlu (2016) combined FAHP
and FTOPSIS, while Keshavarz et al. (2014) use the same combination of methods for prioritisation of
technological competencies to maximise the financial and non-financial performance. Mandic et al. (2014)
analysed financial parameters of Serbian banks through the application of the fuzzy AHP and TOPSIS
methods. Pramanik et al. (2017) dealt with resilient supplier selection using AHP-TOPSIS-QFD under a
fuzzy environment. Tadic et al. (2014) evaluated and ranked the organisational resilience factor by using
FAHP and FTOPSIS. Also, Tadic et al. (2013) used the same methods to evaluate quality goals. Kannan
et al. (2014) used FTOPSIS for selecting a green supplier. Vinodh et al. (2014) integrated FAHP-TOPSIS
for selecting the best plastic recycling method. Lima Junior et al. (2014) compared FAHP and FTOPSIS
methods to supplier selection. Samvredi et al. (2013) integrated FAHP-FTOPSIS to quantify risks in a sup-
ply chain. Onar et al. (2014) used hesitant FTOPSIS and Interval type-2 FAHP for strategic decision se-
lection.

Therefore, in this paper an integrated model that combines the fuzzy AHP method and classical MCDM
method for ranking TOPSIS is applied. The FAHP method is used to determine the priority weights of em-
ployee productivity criteria being analysed, whereas the TOPSIS method is used to rank the electrical com-
panies in Serbia.

The application of the classical MCDM method and fuzzy methods for analysing the electrical power sup-
ply and distribution sector can be found in the following studies. Bas (2013) has proposed the SWOT-fuzzy
TOPSIS methodology combined with AHP for analysis of electricity supply chain in Turkey. Kabir & Sumi
(2014) have integrated FAHP and PROMETHEE methods to select power substation location (case study
from Bangladesh). On the other hand, et al. (2015) used FTOPSIS for ranking renewable energy supply sys-
tems in Turkey. Also, Zare et al. (2015) analysed the electricity supply chain using AHP and FTOPSIS. Choud-
hary & Shankar (2012) have introduced fuzzy AHP-TOPSIS framework for evaluation and selection of thermal
power plant location in India.

3. Sample and Methods

In this section, the integrated multi-criteria model for the analysis of employee productivity in the companies
of the sector D-Electrical power supply operating on the territory of Serbia will be presented. The data con-
sidered are retrieved from the official financial statements displayed on the website of the Agency for Busi-
ness Registers. The study includes the sample of six large companies from the sector D-Electrical power
supply. Four basic criteria were analysed identified by the financial experts pointing to the employee pro-
ductivity: Operating income/Number of employees, Equity/Number of employees, Net income/Number of
employees and Total assets/Number of employees. The model is created integrating two methods of fuzzy
and multi-criteria decision-making such as: Fuzzy Analytic Hierarchy Process – FAHP and Technique for
Order Performance by Similarity to Ideal Solution – TOPSIS. The FAHP method uses the priority vectors for
decision-making criteria. This method uses linguistic variables and thus enables decision makers to repre-
sent the vague statements in a much simpler manner. On the other hand, the TOPSIS method is used for
effectively ranking the alternatives based on the distance from the Positive Ideal Solution (PIS) and Nega-
tive Ideal Solution (NIS). A detailed overview of the employed framework is presented in Appendix and pa-
pers Mandic et al. (2017), Mandic et al. (2014).

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

4. Findings and Results

The first step within the FAHP method defines the research goal, in our case, „The analysis of employee pro-
ductivity in the companies from the sector D-Electrical power supply operating in the territory of Serbia”. For
this purpose, four basic criteria of employee productivity were considered: Operating income/Number of
employees, Equity/Number of employees, Net income/Number of employees and Total assets/Number of
employees. Further, in the second step the priority weights were calculated for each of the criteria individu-
ally using the Logistical scale of importance (Table 1). The linguistic scale of importance (Kilincci & Onal,
2011) shows the manner in which the linguistic variables convert into triangular fuzzy numbers.

Table 1: Linguistic scale of importance

Source: Author’s Analysis

Within Table 2 a comparison is given of four basic criteria of employee productivity using the triangular fuzzy
numbers and their reciprocal values, based on which priority weights were calculated (Wc) for each cri-
terium individually.

Table 2: Fuzzy comparison matrix for four attributes with respect to the objective and its priority vectors

Source: Author’s Analysis

Table 2 shows that in the process of estimating the employee productivity, the criteria Operating in-
come/Number of employees has the highest importance with the weight vector of 0.349; the second is Net
income/Number of employees with 0.300, the third is Total assets/Number of employees with 0.220, whereas
the fourth place belongs to Equity/ Number of employees with 0.131.

Table 3 shows relevant data for the companies in sector D-Electrical power supply retrieved from the fi-
nancial statements of the Agency of Business registers. As shown in Table 3, six large companies from sec-
tor D-Electrical power supply were chosen, operating in the territory of Serbia.

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

Linguistic scale of importance Triangular fuzzy numbers
Reciprocal value of
triangular fuzzy numbers

Equal (1,1,1) (1,1,1)

Weak (1/2,1,3/2) (2/3,1,2)

Fairly Strong (3/2,2,5/2) (2/5, 1/2, 2/3)

Very strong (5/2,3,7/2) (2/7, 1/3, 2/5)

Absolute (7/2,4,9/2) (2/9, 1/4, 2/7)

Criteria
Operating

income/Number
of employees

Equity/Number
of employees

Net
income/Number

of employees

Total
assets/Number
of employees

Priority
vector
(Wc)

Operating
income/Number
of employees

(1,1,1) (3/2,2,5/2) (1/2,1,3/2) (3/2,2,5/2) 0.349548

Equity/Number
of employees

(2/5,1/2,2/3) (1,1,1) (2/5,1/2,2/3) (1/2,1,3/2) 0.131118

Net
income/Number
of employees

(2/3,1,2) (3/2,2,5/2) (1,1,1) (1/2,1,3/2) 0.299606

Total
assets/Number
of employees

(2/5,1/2,2/3) (2/3,1,2) (2/3,1,2) (1,1,1) 0.219728

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

Table 3: Values of the companies productivity

Source: Author’s Analysis

After determining weight vectors for the criteria of productivity of employees using FAHP methodology, the
next step suggested within this paper is using the TOPSIS method for ranking the companies. Within the
TOPSIS method, the first phase is normalisation of decision-making matrix, followed by the calculation of the
weighted normalised matrix so that the normalised matrix is multiplied by FAHP weight vectors for the pro-
ductivity criteria. Then the shortest distance from the PIS and the farthest distance from the NIS are deter-
mined. After calculating PIS and NIS, it is possible to obtain the similarity coefficients (CCi) for each
alternative. Table 4 presents the display parameters PIS, NIS, CCi and Rank for large enterprises. Table 4
shows the parameters PIS, NIS and CCi and Ranking for large companies. The primary goal of the TOPSIS
method is to consider simultaneously both PIS and NIS distances so that at the end the ideal solution is cal-
culated closest to PIS and farthest from NIS.

Table 4: PIS, NIS, CCi and the Ranking of enterprises
Source: Author’s Analysis

Table 4 shows that the most productive operations in large enterprises from sector D-Electrical power sup-
ply were performed by the company PC EPS Beograd, followed by EBD llc Beograd, PC EMS Beograd,
Elektrosrbija llc Kraljevo, Elektrovojvodina llc Novi Sad and finally ED Center llc Kragujevac.

Operating incomes are a key factor in operating profit, and it is of particular importance to financial per-
formance metrics. For measuring the productivity of employees concerning the actual financial perform-
ance on an annual basis in the company, operating incomes are an especially important factor for assessing
the real efficiency of the companies. The structure of total incomes regarding the allocation, and thus the op-
erating income as its integral part, is made of the expenditures of the production elements (cost of items of
work, means of work and labour), as well as gains. The greatest opportunities for increasing labour pro-
ductivity are precisely in an adequate drive of the human factor. In this sense, gaining even greater impor-
tance in the productivity metrics is the operating income criterion. Staff motivation is conditioned by the
manner of rewarding and incentives implemented by the company management.

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Large companies d+ d- Cci Rank

PC EPS BEOGRAD 0 0.464026 1 1

ELEKTROSRBIJA LLC KRALJEVO 0.44883833 0.035058 0.07244865 4

ELEKTROVOJVODINA LLC NOVI SAD 0.45541963 0.011139 0.02387425 5

PC EMS BEOGRAD 0.43947313 0.038114 0.07980507 3

EBD LLC BEOGRAD 0.43712221 0.047745 0.09847014 2

ED CENTER LLC KRAGUJEVAC 0.46402599 0 0 6

It is also necessary to emphasize that excessive workloads placed before the employees can negatively af-
fect the results of the productivity metrics, thus, in addition to monitoring the productivity in the company,
the fluctuation of employees should also be analyzed (number of newly admitted workers in relation to the
total number of employees, the number of employees who left the company in relation to the total number
of employees and the number of replacement workers in relation to the total number of employees). Frequent
employee fluctuation regarding leaving the workplace may indicate that the employees of a particular com-
pany cannot keep the required operating pace as it is defined following the actual standards, in the long run.

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

Conclusion

The primary purpose of this research is to apply a hybrid model which is based on a combination of classical and fuzzy
MCDM methods to analyse the problem of employee productivity in electrical power supply companies of Serbia. The
used model allows for the priority vectors for the selected criteria of productivity of employees to be determined. Besides,
the model also allows ranking of the selected companies. The results of this paper demonstrate the capability and
effectiveness of the proposed model in choosing the most appropriate electrical company in accordance with the analysis
the employee productivity problem.

In the paper, the integrated model combining the two methods of multi-criteria decision analysis was developed: Fuzzy AHP
and TOPSIS. As it can be seen from the study, in the first step we determined the priority weights for the four basic crite-
ria of productivity using the FAHP: Operating income/Number of employees, Equity/Number of employees, Net
income/Number of employees and Total assets /Number of employees. We have concluded that the most important cri-
terion is Operating income/Number of employees with a weight vector of 0.349, the second is Net income/Number of em-
ployees with 0.300, the third is Total assets/Number of employees with 0.220, while the forth place is occupied by
Equity/Number of employees with 0.131. The next step taken in this study is the ranking of large enterprises from sector
D-electrical power supply by using the TOPSIS method. This method enabled the determination of the distances of each
alternative from PIS and NIS, and thus an ideal solution was obtained which was nearest to PIS and farthest from the NIS.
Among large companies, PC EPS Beograd was ranked as a company that achieved the best results according to the se-
lected criteria of productivity, followed by EBD llc Beograd, PC EMS Beograd, Elektrosrbija llc Kraljevo, Elektrovojvodina
llc Novi Sad and, finally, ED Center llc Kragujevac.

The electricity market of the Republic of Serbia remains dominant, depending on the actual trends in the segment of op-
erating incomes, so that in making decisions particular attention should be paid to it, bearing in mind the exposure of the
companies to competition risk. Having also in mind that the market of the Republic of Serbia remains distinctive in that it
is characterized by the pressure of disloyal competition, which in terms of a small number of market participants and the
existence of market concentrations allows a misuse of a dominant position by several largest producers (especially in the
case of restrictions on the transmission network), gives the efficiency increase even greater significance.

The main limitation of this research, is indicated to be the possibility of obtaining better results by combining two fuzzy meth-
ods, or by a combination of three or more MCDM methods. Therefore, future research will be dedicated to combining
more classical and fuzzy MCDM methods to determine whether the development of such models can provide better and
more relevant results in the ranking procedure.

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Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

APPENDIX

FAHP-TOPSIS Framework
Fuzzy Analytic Hierarchy Process (FAHP)

In order to deal with uncertain and imprecise data, numerous FAHP methodologies are proposed in the lit-
erature by various authors (Van Laarhoven & Pedrycz, 1983; Buckley, 1985; Chang, 1996). The FAHP method
was developed for hierarchical problems solving. It represents a systematic approach to selecting alterna-
tives and solving problems using the concept of fuzzy sets theory (Zadeh, 1965) and the AHP method, im-
plemented through the use of triangular fuzzy numbers (Chang, 1996). A fuzzy set is a class of objects
characterised by membership functions, where each object has a membership function in the interval [0,1].

A fuzzy set is usually mark as “ “, and defined by subset with the membership function . Tri-
angular fuzzy numbers are special classes of fuzzy numbers whose membership is defined by three real
numbers, expressed as (l, m, u) (Dubois & Prade, 1978). The symbols (l, m, u) represent the minimum
possible value, the possible value and the maximum possible value, respectively. Triangular fuzzy numbers
are used for the preferences of one criterion over another. Therefore, the Triangular fuzzy scale of preferences
or Linguistic scale of importance is given in Table 1.

The most commonly used is the FAHP methodology which was extensively analysed by Chang (1996): let

be a set of objects, and let be a set of goals. According to the

methodology of extended analysis which was set up by Chang (1996), an extended analysis of goal gi is
performed for every taken object. The values of extended analysis m for each object can be represented
as follows:

(1)

where are fuzzy triangular numbers. Chang’s extended analysis consists of the fol-
lowing steps:

Step 1: The values of fuzzy extensions for the i-th object are given in Expression (2):

(2)

In order to obtain the expression , it is necessary to perform additional fuzzy operations

with values of the extended analysis, which is represented by Expressions (3), (4):

(3)

(4)

In other words, it is necessary to calculate the inverse vector using Expression (5):

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

(5)

Step 2: The degree of possibility for and is defined by Expres-

sion (6):

,
(6)

It can be represented in the following manner by Expression (7):

(7)

where is the ordinate of the highest intersection point between and (Figure 1).

In order to compare and , values of both and are needed.

Figure 1: The intersection between M1 and M2

Step 3: The degree of possibility for a convex fuzzy number to be greater than the k convex numbers
can be defined by Expression (8):

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

(8)

Let us assume that Expression (9) is true:

(9)

for . The weight vector is obtained by Expression (10):

(10)

where consists of n elements.

Step 4: Through normalization, the weight vectors are reduced to Expression (11):

(11)

where W does not represent a fuzzy number (Büyüközkan et al., 2008; Kahraman et al., 2006).

TOPSIS method (Technique for Order Performance by Similarity to Ideal Solution)

The TOPSIS is one of the most used classical multi-criteria decision-making methods. This method is very
useful for real problem solving, providing the optimal solution or the alternatives’ ranking. The TOPSIS ranks
alternatives according to their distance from the Positive ideal solution (PIS) and Negative ideal solution
(NIS). PIS maximises the benefit criteria and minimises the cost criteria, while NIS maximises the cost crite-
ria and minimises the benefit criteria (). The fundamental principle is that the chosen alternative should have
the shortest distance from the PIS and the farthest distance from the NIS (Abo-Sinna & Amer, 2005; Jahan-
shahloo et al., 2006; Shih, Shyur & Lee, 2007; Gumus, 2009).

The TOPSIS methodology presented by (Hwang & Yoon, 1981) consists of the following steps:

Step 1: The decision matrix is normalised through the application of Expression (12):

(12)

Step 2: A weighted normalised decision matrix is obtained by multiplying the normalised matrix with the
weights of the criteria, Expression (13):

(13)

Step 3: PIS (maximum value) and NIS (minimum value) are determined by Expressions (14, 15):

(14)

(15)

Step 4: The distance of each alternative from PIS and NIS is calculated using Expressions (16), (17):

(16)

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

Management: Journal of Sustainable Business and Management Solutions in Emerging Economies 2017/22(2)

About the Author

(17)

Step 5: The closeness coefficient for each alternative (CCi) is calculated by applying Expression (18):

(18)

Step 6: At the end of the analysis, the ranking of alternatives is made possible by comparing the (CCi)
values.

(Received/Accepted)
(January 2017 / July 2017)

Snežana Knežević
University of Belgrade, Faculty of Organizational Sciences, Serbia

knezevic.snezana@fon.bg.ac.rs

Snežana Knežević was born in Pančevo (Jabuka), where she finished school of
economics. She graduated from the Faculty of Economics at the University of Belgrade,

where she also got her MSc degree. She got her PhD degree at the Faculty of
Organizational Sciences at the University of Belgrade. Her fileds of interest include

accounting, financial analysis, and valuation. She is bilingual fluency in both English
and French. She has published several monographs and she has produced over 50

papers of scientific and professional orientation in the country and abroad. She is
currently working at the Faculty of Organizational Sciences in Belgrade, Department of
Financial Management and Accounting as an Associate professor. She is the owner of

the Agency for accounting and consulting services.

Ksenija Mandić
University of Belgrade, Faculty of Organizational Sciences, Serbia

Ksenija Mandić received her BSc, MSc and the PhD degrees in Faculty of
Organizational Science from the University of Belgrade, Serbia, in 2006, 2008 and 2015

respectively. She works in telecommunication company Crony since 2007. Her research
interests are decision making theory, supply chain management, multi-criteria decision

making methods, fuzzy logic and Interpolative Boolean Algebra.

Snežana Knežević, Ksenija Mandić, Aleksandra Mitrović, Veljko Dmitrović, Boris Delibašić 2017/22(2)

Aleksandra Mitrović
University of Kragujevac, Faculty of Hotel Management and Tourism

aleksandra.stankovic@kg.ac.rs

Aleksandra Mitrović, Ph.D., works as a Assistant Professor at the Faculty of Hotel
Management and Tourism in Vrnjačka Banja, University of Kragujevac. She completed

her Bachelor Studies in Accounting and Corporate Finance as well as her Master
studies at the Faculty of Economics in Kragujevac. She got her PhD degree in 2016. The

fields of her scientific and professional interests are related to Accounting and Finance.

Veljko Dmitrović
University of Belgrade, Faculty of Organizational Sciences, Serbia

dmitrovicv@fon.bg.ac.rs

Veljko Dmitrović works at the Faculty of Organizational Sciences, University of Belgrade,
at the Department of Financial Management and Accounting as assistant professor. He

achieved PhD degree at the Faculty of Organizational Sciences. He achieved his MSc
degree in Financial Management at the Faculty of Organizational Sciences, University of

Belgrade, and his BSc and MA degrees in Marketing Management at the Faculty of
Economics in Subotica, University of Novi Sad. So far he has authored and coauthored
more than 50 papers published in international and national journals and conferences.

He has been involved in several research projects. Before the academic career he
gained practical experience working for five years in “Fidelinka” a.d., Subotica.

Boris Delibašić
University of Belgrade, Faculty of Organizational Sciences, Serbia

boris.delibasic@fon.bg.ac.rs

Boris Delibašić is professor at the University of Belgrade - Faculty of Organizational
Sciences, Serbia. His research interests lie in business intelligence, data mining,

machine learning, multicriteria decision analysis, and decision support systems. He
serves in editorial boards of several international journals. He is a coordinator of the

EURO working group on Decision Support Systems. He obtained his PhD in 2007 from
the University of Belgrade. He was awarded with the Fulbright Visiting Scholar Grant in

2011. He speaks fluently English, and German, and speaks also Russian,
French, and Italian. His research profile is available at
https://www.researchgate.net/profile/Boris_Delibasic

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/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [623.622 850.394]
>> setpagedevice