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D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
149
Stanujkic, D., Karabasevic, D., Smarandache, F., Zavadskas, E.K.,
Maksimovic, M. (2019), “An Innovative Approach to Evaluation of the
Quality of Websites in the Tourism Industry: a Novel MCDM Approach
Based on Bipolar Neutrosophic Numbers and the Hamming Distance”,
Transformations in Business & Economics, Vol. 18, No 1 (46), pp.149-
162.
AN INNOVATIVE APPROACH TO EVALUATION OF THE
QUALITY OF WEBSITES IN THE TOURISM INDUSTRY: A
NOVEL MCDM APPROACH BASED ON BIPOLAR
NEUTROSOPHIC NUMBERS AND THE HAMMING
DISTANCE
1Dragisa Stanujkic
University of Belgrade
Technical Faculty in Bor
Vojske Jugoslavije 12
19210 Bor
Serbia
E-mail: dstanujkic@tfbor.bg.ac.rs
2Darjan Karabasevic
University Business Academy in
Novi Sad
Faculty of Applied Management,
Economics and Finance
Jevrejska 24
11000 Belgrade
Serbia
E-mail: darjan.karabasevic@mef.edu.rs
3Florentin Smarandache
University of New Mexico
Department of Mathematics
705 Gurley Avenue
Gallup, NM 87301
USA
E-mail: fsmarandache@gmail.com
4Edmundas Kazimieras
Zavadskas
Vilnius Gediminas Technical
University
Institute of Sustainable Construction,
Labour of Operational Research
Faculty of Civil Engineering
Saulėtekio al. 11
LT-10223 Vilnius
Lithuania
E-mail: edmundas.zavadskas@vgtu.lt
5Mladjan Maksimovic
University Business Academy in Novi Sad
Faculty of Applied Management, Economics and Finance
Jevrejska 24
11000 Belgrade
Serbia
E-mail: mladjan.maksimovic@mef.edu.rs
1Dragisa Stanujkic, PhD, is an Associate Professor of
Information Technology and Decision Sciences at the
Technical Faculty in Bor, University of Belgrade. His current
research is focused on decision-making theory, expert systems
and intelligent decision support systems.
2Darjan Karabasevic, PhD, is an Assistant Professor and a
Vice-Dean for research and development at the Faculty of
Applied Management, Economics and Finance, University
Business Academy in Novi Sad. His current research is
focused on the management, informatics and decision-making
theory.
---------TRANSFORMATIONS IN --------
BUSINESS & ECONOMICS
© Vilnius University, 2002-2019
© Brno University of Technology, 2002-2019
© University of Latvia, 2002-2019
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
150
3Florentin Smarandache, PhD, is a Professor of mathematics
at the University of New Mexico, USA. He has published
many papers and books on neutrosophic set and logic and their
applications and has presented to many international
conferences. He got his MSc in Mathematics and Computer
Science from the University of Craiova, Romania, PhD from
the State University of Kishinev, and Post-Doctoral in Applied
Mathematics from Okayama University of Sciences, Japan.
4Edmundas Kazimieras Zavadskas, PhD, Prof., the Head of
the Institute of Sustainable Construction at Vilnius Gediminas
Technical University, Lithuania. PhD in Building Structures
(1973). Dr. Sc. (1987) in Building Technology and
Management. A member of Lithuanian and several foreign
Academies of Sciences. Doctore Honoris Causa from Poznan,
Saint-Petersburg and Kiev universities. A member of
international organizations; a member of steering and
programme committees at many international conferences; a
member of the editorial boards of several research journals; the
author and co-author of more than 400 papers and a number of
monographs in Lithuanian, English, German and Russian.
Research interests: building technology and management,
decision-making theory, automation in design and decision
support systems.
5Mladjan Maksimovic, PhD, is an Assistant Professor and a
Chairman of the Quality Committee at the Faculty of Applied
Management, Economics and Finance, University Business
Academy in Novi Sad. His current research is focused on
informatics, management and quality.
Received: April, 2018
1st Revision: May, 2018
2nd Revision: October, 2018
Accepted: January, 2019
ABSTRACT
. Nowadays, the performance and business
operations of organizations are closely linked to the quality of their
websites compared to the competition. With growing market
competition, the quality of websites becomes a significant
component and is increasingly being explored and identified as the
main factor of comparative advantage over the competition and the
maintenance of good customer relationships. A multiple criteria
decision-making approach based on the use of bipolar neutrosophic
numbers and the Hamming distance is proposed in this paper. The
main aim of this article is to emphasize the fact that MCDM models
with a smaller number of criteria can be formed without a loss of
precision by applying bipolar neutrosophic numbers. In addition to
this, the three variants for ranging bipolar neutrosophic numbers
based on the Hamming distance and a distance from the ideal point
are proposed. The applicability of the proposed approach is
considered in the case of website evaluation.
KEYWORDS
: bipolar neutrosophic set, Hamming distance,
MCDM.
JEL classification
: D81, C61, C44.
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
151
Introduction
The beginnings of the Internet use in tourism are considered to be the revolutionary
changes that have completely transformed the tourism sector. Today, an increasing number of
customers avoid traditional intermediaries when buying products and services in tourism –
customers first obtain information on products and services and then buy them online.
The rapid developments of the Internet, the expansion of its availability and its
integration with other technologies have led to significant changes in consumer behaviour
when buying products and services in tourism (Verma, 2010).
Nowadays, the performance and business operations of organizations are closely
linked to the quality of their websites compared to the competition. With growing market
competition, the quality of websites becomes a significant component and is increasingly
being explored and identified as the main factor of comparative advantage over the
competition. Websites could be also important for maintenance of good customer
relationships.
Therefore, the measuring of the quality of an organization’s website is of particular
importance for the organization. Based on the evaluation of the website quality, organizations
may receive feedback on the segment which they need to improve in order to be ahead of the
competition. The significance of the quality evaluation, especially when websites are
concerned, are highlighted by Hsu et al., (2018), Abbasi et al., (2018), Chen et al., (2017),
Tian, Wang (2017), Wang et al. (2015), Al-Qeisi et al. (2014), Parasuraman et al. (1985) and
so on. A Multiple Criteria Evaluation (MCE), often referred to as Multiple Criteria Decision
Analysis (MCDA), refers to the evaluation of alternatives in relation to several our often
mutually conflicting criteria of a larger number.
Compared to Multiple Criteria Decision Making (MCDM), which is usually carried
out with the aim of selecting one out of a set of available alternatives, the primary goal of the
MCE is more often the ranking or determination of the relative importance of alternatives.
Such an approach can be very useful in a competitive environment, especially when taking
into consideration the fact that the entry of new players may affect the positions of the
existing players in the market.
In the MCE, as well as in the MCDM, the selected set of evaluation criteria and their
relative significance have a significant impact on the results of the evaluation. It is also known
that a more accurate evaluation can be made by using a greater number of evaluation criteria.
However, an increase in the number of the evaluation criteria can affect the increasing
complexity of a proposed decision-making model, which can have a negative impact on the
effectiveness and real usage of proposed MCE models.
Certain possibilities of forming the decision-making models based on the use of a
smaller number of evaluation criteria, without losing precision, can be obtained based on the
use of grey, fuzzy or neutrosophic numbers. In the decision-making models formed in such a
manner, certain types of grey, fuzzy or neurotrophic numbers can be used to collect the ratings
obtained from respondents.
Therefore, the rest of this article is structured as follows: in the first section, some
significant elements of the neutrosophic sets theory are considered, with a special emphasis on
the bipolar neutrosophic sets, whereas in the second section, certain approaches to the
evaluation of websites are considered, with the aim of defining an effective set of evaluation
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
152
criteria containing as small a number of evaluation criteria as possible. In Section Three, a
framework for the evaluation of the quality of websites is proposed, and in Section Four, its
use is illustrated with the aim to demonstrate its practical usability. Finally, conclusions are
given.
1. The Basic Concepts of a Bipolar Neutrosophic Set
As is previously mentioned, Zadeh (1965) proposed fuzzy set theory and introduced
the membership function.
Definition 1. A Fuzzy Set (Zadeh, 1965). Let X be a nonempty set. Then, a fuzzy set
A in X is a set of ordered pairs:
= XxxxA A )( ,
, (1)
where the membership function
)(x
A
+
denotes the degree of the membership of an
element x to the set A, and
1] ,0[)( x
A
.
Atanassov (1986) extended the concept of fuzzy set theory and introduced
intuitionistic fuzzy sets, which are characterized by using the membership and non-
membership functions.
Definition 2. An Intuitionistic Fuzzy Set (Atanassov, 1986). Let X be a nonempty
set. Then, an intuitionistic fuzzy set is defined as follows:
= XxxxxA AA )(),( ,
, (2)
where:
)(x
A
and
)(x
A
represent the degree of the membership and the degree of the
non-membership of the element x to the set A, respectively;
1] ,0[)( x
A
and
1] ,0[)( x
A
,
where
)(xA
and
)(xA
satisfy the following condition
.1)()(0 + xx AA
In Intuitionistic Set Theory, Atanassov (1986) also implicitly introduced the
indeterminacy-membership function
)(x
A
, which is defined as
)()(1)( xxx AAA
−−=
.
Lee (2000) introduced the notion of bipolar fuzzy sets by extending the concept of
fuzzy sets, where the degree of the membership is expanded from [0, 1] to [-1, 1].
Definition 3. A Bipolar Fuzzy Set (Lee, 2000). Let X be a nonempty set. Then, a
bipolar fuzzy set is defined as follows:
= −+ XxxxxA AA )(),( ,
, (3)
where: the positive membership function
)(x
A
+
denotes the satisfaction degree of the
element x to the property corresponding to a bipolar-valued fuzzy set, and the negative
membership function
)(x
A
−
, denotes the degree of the satisfaction degree of the element x to a
corresponding complementary bipolar-valued fuzzy set, respectively;
]1 ,0[: →
+X
A
and
]0 ,1[: −→
−X
A
.
Smarandache (1999) introduced the neutrosophic sets theory, as the generalization of
fuzzy sets and intuitionistic fuzzy sets.
Definition 4. Neutrosophic Sets (Smarandache, 1999). Let X be a nonempty set.
Then, Neutrosophic Set (NS) A in X is defined as:
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
153
= XxxFxIxTxA AAA )(),(),( ,
, (4)
where: TA(x), IA(x) and FA(x), denote the truth-membership TA(x), the indeterminacy-
membership IA(x) and the falsity-membership functions FA(x), and
[1,0]:,, +−
→XFIT AAA
.
In contrast to intuitionistic sets, the restriction regarding to the sum of the membership
functions is eliminated, so that
−0
TA(x)+IA(x)+UA(x)
+
3
.
In 2015, Deli et al. (2015) introduced Bipolar Neutrosophic Sets (BNS) by
generalizing the concept of bipolar fuzzy sets. Deli et al. (2015) also defined the Score,
Certainty and Accuracy functions, as well as the Bipolar Neutrosophic Weighted Average and
the Bipolar Neutrosophic Weighted Geometric operators for the BNS.
Definition 5. Bipolar Neutrosophic Sets (Deli et al., 2015). Let X be a nonempty set.
Then, a BNS A in X is as follows:
= −−−+++ XxxFxIxTxFxIxTxA AAAAAA )(),(),(),(),(),( ,
, (5)
where:
)(),(),(xFxIxT +++
denote the membership, the indeterminate membership and
the falsity membership of x to the BNS A, and
)(),(),(xFxIxT −−−
denote the membership, the
indeterminate membership and the falsity membership of x to a complemenry BNS;
]0,1[:,, →
+++ XFIT
and
]0,1[:,, −→
−−− XFIT
.
Deli et al. (2015) also introduced the Bipolar Neutrosophic Number (BNN), which can
be denoted as follows
= −−−+++ fitfita , , ,, ,
for convenience.
Definition 6. (Deli et al., 2015) Let
= −−−+++ 1111111 , , ,, , fitfita
and
= −−−+++ 2222221 , , ,, , fitfita
be two BNNs and
0
. The basic operations for these numbers are
as follows:
−−−−−−−−−−+=+++++++++−−++++++++ )(),(,,,, 21212121212121212121 ffffiiiittffiittttaa
(6)
−−−−−−−+−+=−−−−−−−−++++++++++ 21212121212121212121 ,),(,,, ffiittttffffiiiittaa
(7)
−−−−−−−−−−= −−−+++ )))(1(1(,)(,)(,)(,)(,)1(1 1111111
fitfita
(8)
−−−−−−−−−−−−= −−−+++
)(,)(),))(1(1(,)1(1 ,)1(1 ,)( 1111111 fitfita
(9)
Definition 7. (Deli et al., 2015) Let
= −−−+++ fitfita , , ,, ,
be a BNN. The score
function s(a) of an BNN is as follows:
6/)111(
)( +−−+++ −−++−+−+= fitfits a
. (10)
Definition 8. (Deli et al., 2015) Let
= −−−+++
jjjjjjj fitfita , , ,, ,
be a collection of BNNs.
The Bipolar Neutrosophic Weighted Average Operator (Aw) of the n dimensions is a mapping
QQA nw →:
as follows:
−−−−−−−−−−−−=
=
= = = = =
−−−++
=
+
=
n
j
n
j
n
j
n
j
n
j
w
j
w
j
w
j
w
j
w
j
n
j
w
j
n
jjjnw
jjjjjj fitfit
awaaaA
1 1 1 1 11
1
21
)))(1(1(),))(1(1(,)(,)(,)(,)1(1
),...,,(
,(11)
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
154
where: wj is the element j of the weighting vector,
]1 ,0[
j
w
and
1
1=
=
n
jj
w
.
Definition 8. Let
= −−−+++ 1111111 , , ,, , fitfita
and
= −−−+++ 2222222 , , ,, , fitfita
be two BNNs.
The Hamming distance between a1 and a2 is as follows:
−+−+−+−+−+−= −−−−−−++++++ ||||||||||||
6
1
),( 21212121212121 ffiittffiittaadH
(12)
2. Choosing Criteria for Evaluating Websites
In a business environment, websites can have different purposes. Moreover, a website
must often play multiple roles, such as: providing information to customers, acquiring and
retaining new customers, and so on. In addition to the said, the fact that customers cannot be
treated as homogeneous groups and that specific customer groups can have their own specific
needs and requirements should not be ignored.
Therefore, designing, developing and maintaining an adequate website is not an easy
task to do at all. After using a website for the very first time, many useful pieces of
information about its functionality can be obtained by using the website’s analytics tools, as
well as visitors’ comments.
Additionally, based on the Service Quality Model, i.e. the SERVQUAL Model,
proposed by Parasuraman et al. (1998), several specialized models for the evaluation of
websites were proposed, such as: WebQyal (Barnes, Vidgen 2000), SITEQUAL (Yoo,
Donthu, 2001), eTailQ (Wolfinbarger, Gilly, 2001) and E-S-SERVQUAL (Parasuraman et al.,
2005). The alleged models, as well as the other models developed based on them, are
successfully used to evaluate numerous websites, particularly so e-commerce, e-marketing
and e-banking websites.
As a significant characteristic of the above-mentioned models, it can be emphasized
that they use several dimensions and sub-dimensions for determining customer satisfaction. In
the MCA and/or MCDM terminology, this means that evaluation is based on the use of
multiple criteria, which have their own sub-criteria.
The evaluation models based on the use of MCDM methods can also be emphasized as
a significant approach to the determination of the quality of websites. For example, Sun, Lin
(2009) evaluated shopping websites by used fuzzy TOPSIS method, whereas Tsai (2010)
evaluated a national park website by using the ANP and VIKOR methods.
These are not isolated research studies related to the use of the MCDM methods for
evaluating websites. The following can be mentioned as some of earlier studies: Lee, Kozar
(2006) and Bilsel et al. (2006), who used the AHP and PROMETHEE II for websites ranking.
There are also a number of recent research studies, such as those by: Abdel-Basset et
al. (2018), who used the VIKOR method and neutrosophic numbers for evaluating e-
government websites; and Stanujkic et al. (2017), who proposed a group multiple-criteria
approach for evaluating hotels’ websites, based on the use of triangular intuitionistic fuzzy
numbers. Stanujkic et al. (2016) also proposed an approach for evaluating websites quality,
based on the use of single-valued neutrosophic numbers.
As has been mentioned earlier, the selected set of evaluation criteria can significantly
affect the characteristics of a proposed MCA/MCDM model. Therefore, the problem of
selecting an adequate set of evaluation criteria for evaluating website has been considered in
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
155
many previous studies. Kapoun (1998) and Lydia (2009) can be mentioned as some of such
studies.
According to Kapoun (1998), the following criteria can be used for evaluating a
website: Accuracy, Authority, Objectivity, Currency, and Coverage. Kapoun’s set of criteria
is often used, and based on it, similar sets of criteria are proposed. For example, Lydia (2009)
adds the sixth criterion, Appearance, while the CRAAP test is proposed at the California State
University of Chico, which suggests the use of the following criteria: Currency, Relevance,
Authority, Accuracy, and Purpose.
However, there are also studies where appropriate, or specialized, sets of criteria are
proposed for the evaluation of different types of websites. For example, Chung, Law (2003)
proposed the following six criteria for evaluating websites in the hotel industry: Facilities
Information, Customer Contact Information, Reservation Information, Surrounding Area
Information, and Website Management, and for each criterion, appropriate sub-criteria are
defined. Contrary to this, Herrero, San Martin (2012) suggested that only three criteria,
namely: Information, Interactivity, and Navigability should be used.
A set of criteria proposed by the Webby Awards
1
, can also be listed as a significant set
of criteria for evaluating websites. This set of criteria includes the following criteria: Content,
Structure and Navigation, Visual Design, Interactivity, Functionality, Innovation, and Overall
Experience.
As a result, there are different approaches to selecting the criteria for websites
evaluation: the use of a number of criteria and sub-criteria contrary to the use of a smaller
number of criteria; the use of a standard set of criteria against the use of specialized sets of
criteria, etc.
The choice of an appropriate set of evaluation selection criteria is very important for
the successful solving of each MCA/MCDM problem. The use of a larger number of criteria
usually leads to the formation of more precise models; on the one hand, a larger number of
criteria can be less desirable if certain data should be collected through a survey.
In contrast to the said, a smaller number of criteria can be much more efficient when
certain data should be collected through a survey, on the one hand, whereas on the other, the
usage of a smaller number of criteria may require the use of significantly more complex
criteria.
Neutrosophic numbers, particularly bipolar neutrosophic numbers, contain more
information than crisp numbers, or fuzzy numbers, for which reason their application can be
very beneficial when a small number of evaluation criteria are used.
Therefore, in this approach, the following three criteria are selected out of the set
proposed by the Webby Awards: Structure and Navigation, Content and Visual Design.
3. The Alternative Procedure for Ranking Alternatives Based on the Hamming Distance
Deli et al. (2015) proposed a MCDM approach to the selection of the best alternative
based on the use of the score, certainty and accuracy functions, as well the Aw and Gw
operators.
In this paper, an approach based on the use of the Hamming distance is proposed. The
detailed step-by-step procedure of the proposed approach can be described through the
1
http://webbyawards.com/judging-criteria/
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
156
following steps:
Step 1. Identify available alternatives and select a set of evaluation criteria. In this
step, a team of experts identifies a set of available alternatives and defines the criteria for their
evaluation.
Step 2. Determine the relative importance of evaluation criteria. In the literature,
many techniques are proposed for determining the weights of criteria, such as pair-wise
comparisons (Saaty, 1980), SWARA (Kersuliene et al., 2010), the Best-Worst Method
(Rezaei, 2015), R-SWARA (Zavadskas et al., 2018) and PIPRECIA (Stanujkic et al., 2017).
In this approach, any of the mentioned techniques can be used for determining the weights of
the criteria.
Step 3. Construct a bipolar neutrosophic decision-making matrix, and do it for each
decision-maker. In this step, each decision-maker forms his/her evaluation matrix, in which
matrix alternatives are evaluated by using BNNs. As a result of these activities, each decision-
maker forms his/her evaluation matrix, whose elements are BNNs.
The specificity of the BNSs is used in this step to perform a two-phase evaluation of
the alternatives in relation to each criterion, where satisfaction is measured in the first phase
and dissatisfaction in the second.
By using such an approach, respondents are enabled to carry out a sufficiently precise
evaluation based on a smaller number of evaluation criteria.
Step 4. Construct a group bipolar neutrosophic decision-making matrix. The
integration of the individual evaluation matrices into a group decision-making matrix can be
carried out by using an aggregation operator. In this approach, the use of the Aw aggregation
operator is proposed for aggregating individual evaluation matrices into a group decision-
making matrix.
After this step, the most appropriate alternative can be determined in several ways. As
one of the most commonly used approaches, the approach based on the use of the score
function can be specified. In such an approach, the value of the score function of each of the
considered alternatives could be determined by applying Eq. (10). After that, the alternative
with the highest value of the score function is the most acceptable one.
In addition to this, an increasing use of fuzzy sets theory, as well as its previously
mentioned extensions, has had a significant impact on proposing the numerous extensions of
the TOPSIS and VIKOR methods, as well as the extensions of the other MCDM methods. As
a result, some other approaches are often proposed, out of which the approaches based on the
distance from the ideal point can be especially emphasized. Therefore, as an alternative to
applying the score function for ranking alternatives, the three variants of the distance-based
approaches are considered in the remaining part of the paper, where all of the three variants
are based on the Hamming distance.
The first variant. In the first of the three proposed variants, the ideal point is formed
as follows:
=
+1 ,0 ,0 ,0 ,0 ,1a
. After that, the Hamming distances of the alternatives to the
ideal point are determined by applying Eq. (12).
In this approach, the alternative with the smallest Hamming distance is the most
preferable one.
The second variant. In the second variant, the ideal point is determined much more
realistically, i.e. in the following manner:
= −−−++++ ij
i
ij
i
ij
i
ij
i
ij
i
ij
ifitfita min,max,max,min,min,max
(13)
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
157
After that, similarly as in the first variant, the Hamming distance is determined for
each alternative, and the best alternative is that with the smallest distance from the ideal point.
The third variant. Unlike the previous two variants, the third variant is based on the
use of the well-known approach proposed in the TOPSIS method, i.e. the determination of the
distances of the alternatives from the ideal and the anti-ideal points, and the determination of
the relative closeness Ci of each such alternative, as follows:
−+
−
+
=
ii
i
idd d
c
(14)
In the proposed approach,
+
i
d
and
−
i
d
denote the Hamming distance of the alternative i
from the ideal and the anti-deal points, respectively, the ideal point being determined as in the
previous variant, and the anti-ideal point being determined as follows:
= −−−++++ ij
i
ij
i
ij
i
ij
i
ij
i
ij
ifitfita max,min,min,max,max,min
(15)
Finally, the most acceptable alternative based on the third variant is the alternative that
has the highest Ci.
4. A Numerical Illustration
In this numerical illustration, the proposed approach is used to evaluate the websites of
the four regional tourism organizations, at the following web addresses:
− http://tookladovo.rs,
− http://www.toom.rs,
− http://tobor.rs, and
− http://toon.org.rs.
The evaluation was made in order to compare the quality of the website of one of the
mentioned tourism organizations in relation to the others, whereby the respondents were not
awarded with the main goal of the evaluation in advance. For the same reason, the order of the
alternatives in the remaining segment of the numerical example is not identical with the
appearance of the aforementioned alternatives.
In order to create the conditions for conducting this study, several potential
respondents were introduced by applying bipolar intuitionist sets and the SWARA method.
For the purpose of this consideration, the responses obtained from the three selected
respondents are chosen. The opinions related to the weights of the criteria, the weights of
criteria and the ratings obtained from the first of the three respondents are presented in Table
1 and Table 2.
Table 1. The opinions and the weights of the criteria obtained from the first of the three respondents
Criteria
sj
kj
qj
wj
Structure and Navigation
C1
1.00
1.00
0.30
Content
C2
1.20
0.80
1.25
0.37
Visual Design
C3
0.90
1.10
1.14
0.34
2.90
3.39
Source: own calculations.
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
158
Table 2. The ratings obtained from the first of the three respondents
C1
C2
C3
wj
0.30
0.37
0.34
A1
<0.7, 0.2, 0.3, -0.3, 0, 0>
<0.7, 0, 0.1, -0.2, 0, 0>
<0.7, 0.1, 0, -0.3, 0, 0>
A2
<0.7, 0, 0.2, -0.2, 0, -0.1>
<0.6, 0, 0.1, -0.3, 0, 0>
<0.4, 0, 0.2, -0.2, 0, 0>
A3
<0.6, 0, 0, -0.7, 0, 0>
<0.7, 0, 0, -0.4, 0, 0>
<0.4, 0, 0.2, -0.2, 0, 0>
A4
<0.9, 0, 0, -0.7, 0, 0>
<0.3, 0.2, 0, -0.1, 0, 0>
<0.6, 0, 0, 0, 0, 0>
Source: own calculations.
The opinions obtained from the three surveys, as well as the appropriate weights, are
accounted for in Table 3.
Table 3. The opinions and the weights of criteria obtained from the three respondents
E1
E1
E1
sj
wj
sj
wj
sj
wj
C1
0.30
0.34
0.38
C2
1.20
0.37
1.00
0.34
1.10
0.34
C3
0.90
0.34
0.90
0.31
1.20
0.28
Source: own calculations.
The group criteria weights calculated as the average value of the criteria weight from
Table 3 are shown in Table 4.
Table 4. The group criteria weights
wj
C1
0.34
C2
0.35
C3
0.31
Source: own calculations.
The ratings of the alternatives expressed in terms of the BNNs obtained from the
second and the third respondents are given in Table 5 and Table 6.
Table 5. The ratings obtained from the second respondent
C1
C2
C3
A1
<0.7, 0.2, 0.3, -0.3, 0, 0>
<0.7, 0, 0.1, -0.2, 0, 0>
<0.7, 0.1, 0, -0.3, 0, 0>
A2
<0.7, 0, 0.2, -0.2, 0, -0.1>
<0.6, 0, 0.1, -0.3, 0, 0>
<0.4, 0, 0.2, -0.2, 0, 0>
A3
<0.6, 0, 0, -0.7, 0, 0>
<0.7, 0, 0, -0.4, 0, 0>
<0.4, 0, 0.2, -0.2, 0, 0>
A4
<0.9, 0, 0, -0.7, 0, 0>
<0.3, 0.2, 0, -0.1, 0, 0>
<0.6, 0, 0, 0, 0, 0>
Source: own calculations. Table 6. The ratings obtained from the third respondent
C1
C2
C3
A1
<0.7, 0.2, 0.3, -0.3, 0, 0>
<0.9, 0, 0, 0, 0, 0>
<0.5, 0, 0.1, -0.2, 0, 0>
A2
<0.7, 0, 0.2, -0.2, 0, -0.1>
<0.9, 0, 0.3, -0.1, 0, 0>
<0.5, 0, 0, -0.3, 0, 0>
A3
<0.6, 0, 0, -0.7, 0, 0>
<0.9, 0, 0.2, -0.5, 0, -0.3>
<0.5, 0, 0, -0.7, 0, -0.2>
A4
<0.9, 0, 0, -0.7, 0, 0>
<0.3, 0.2, 0, 0, 0, 0>
<0.5, 0, 0, 0, 0, 0>
Source: own calculations.
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
159
The group ratings calculated by applying Eq. (11) are accounted for in Table 7. In this
calculation, the following weights are assigned to the respondents: wE1=0.35, wE2=0.33, and
wE3=0.32.
Table 7. The group ratings
C1
C2
C3
A1
<0.7, 0.2, 0.3, -0.3, 0, 0>
<0.79, 0, 0, 0, 0, 0>
<0.65, 0, 0, -0.26, 0, 0>
A2
<0.7, 0, 0.2, -0.2, 0, -0.85>
<0.74, 0, 0.14, -0.21, 0, 0>
<0.43, 0, 0, -0.23, 0, 0>
A3
<0.6, 0, 0, -0.7, 0, 0>
<0.79, 0, 0, -0.43, 0, -0.68>
<0.43, 0, 0, -0.3, 0, -0.6>
A4
<0.9, 0, 0, -0.7, 0, 0>
<0.3, 0.2, 0, 0, 0, 0>
<0.57,0,0,0,0,0>
Source: own calculations.
The overall ratings calculated by applying Eq. (11), as well as the ranking order of the
alternatives, are presented in Table 8.
Table 8. The overall ratings, the score and the ranking order of the considered alternatives
Overall ratings
Si
Rank
A1
<0.72, 0, 0, 0, 0, 0>
3.72
3
A2
<0.65, 0, 0, -0.21, 0, -0.95>
4.39
1
A3
<0.64, 0, 0, -0.45, 0, -0.98>
4.17
2
A4
<0.69, 0, 0, 0, 0, 0>
3.69
4
Source: own calculations.
As can be seen from Table 8, the most acceptable alternative based on the Score
Function is the alternative denoted as A2.
The results achieved by using the Hamming distance and the three proposed variants
are considered in the rest of this section. The results obtained by using the first of the three
considered variants are demonstrated in Table 9.
Table 9. The overall ratings, the Hamming distances and the ranking order of the considered alternatives
Overall ratings
dH
Rank
a+
<1, 0, 0, 0, 0, 0>
A1
<0.72, 0, 0, 0, 0, 0>
0.21
3
A2
<0.65, 0, 0, -0.21, 0, -0.95>
0.10
1
A3
<0.64, 0, 0, -0.45, 0, -0.98>
0.14
2
A4
<0.69, 0, 0, 0, 0, 0>
0.22
4
Source: own calculations.
As can be seen from Table 9, the ranking orders obtained by using the Score Function
and the first of the three proposed variants based on the Hamming distance are identical.
The results obtained by using the second of the three considered variants are shown in
Table 10.
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
160
Table 10. The ranking of the alternatives based on the second of the three proposed variants
Overall ratings
dH
Rank
a+
<0.72, 0, 0, 0, 0, -0.98>
A1
<0.72, 0, 0, 0, 0, 0>
0.16
3
A2
<0.65, 0, 0, -0.21, 0, -0.95>
0.05
1
A3
<0.64, 0, 0, -0.45, 0, -0.98>
0.09
2
A4
<0.69, 0, 0, 0, 0, 0>
0.17
4
Source: own calculations.
As can be seen from Table 10, the ranking orders obtained by using the second variant
of the three proposed variants based on the Hamming distance is the same as in the previously
considered cases. However, we should be careful because Stanujkic (2013) indicates that, in
some cases, the ideal point may have an effect on the ranking order of alternatives.
Ultimately, the results obtained by applying the third proposed variant are shown in
Table 11.
Table 11. The ranking of the alternatives based on the third of the three proposed variants
Overall ratings
+
i
d
−
i
d
-
Ci
Rank
a+
<0.72, 0, 0, 0, 0, -0.98>
a-
<0.64, 0, 0, -0.45, 0, 0>
A1
<0.72, 0, 0, 0, 0, 0>
0.16
0.09
0.35
3
A2
<0.65, 0, 0, -0.21, 0, -0.95>
0.05
0.20
0.79
1
A3
<0.64, 0, 0, -0.45, 0, -0.98>
0.09
0.16
0.65
2
A4
<0.69, 0, 0, 0, 0, 0>
0.17
0.08
0.33
4
Source: own calculations.
The results shown in Table 11 also confirm the fact that the ranking results obtained
by using the third variant based on the Hamming distance are identical with the results
obtained by using the procedure for ranking BNNs, proposed by Deli et al. (2015).
Conclusion
Bipolar neutrosophic numbers contain more information than the other types of fuzzy
or crisp numbers. In addition, these numbers can be used to carry out a two-phase evaluation
of the alternative in relation to the selected criteria, where satisfaction is measured in the first
phase and dissatisfaction in the second.
By applying such an approach, respondents are enabled to perform a sufficiently
precise evaluation, based on a smaller number of criteria.
However, it should be emphasized that the use of bipolar neutrosophic numbers is not
so simple in the case of pre-unmanaged subjects.
This paper also proposes a group multiple criteria approach based on the Hamming
distance application. The numerical illustration shows that the application of this approach
generates the same ranking results as is the case with the application of the Score, which
confirms the applicability of the proposed approach.
D. Stanujkic, D. Karabasevic,
F. Smarandache, E.K. Zavadskas,
M. Maksimovic
ISSN 1648-4460
Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
161
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Satisfaction and Behavioural Intentions of Tourist: Principles and Case Studies
TRANSFORMATIONS IN BUSINESS & ECONOMICS, Vol. 18, No 1 (46), 2019
162
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NAUJAS POŽIŪRIS Į VERTYBINĮ TURIZMO SEKTORIAUS SVETAINIŲ VERTINIMĄ:
BIPOLINIAIS NEUTROSOFINIAIS SKAIČIAIS IR HEMINGO ATSTUMU GRINDŽIAMAS NAUJAS
KOMBINUOTAS DAUGIAKRITERINIŲ SPRENDIMŲ PRIĖMIMO METODAS
Dragisa Stanujkic, Darjan Karabasevic, Florentin Smarandache, Edmundas Kazimieras Zavadskas,
Mladjan Maksimovic
SANTRAUKA
Šiandienos organizacijų darbas ir jų veikla yra glaudžiai susijusi su jų svetainių kokybe dėl konkurencijos.
Augant konkurencijai rinkoje, interneto svetainių kokybė tampa svarbia dedamąja bei vis dažniau tiriama ir
nurodoma kaip pagrindinis santykinio pranašumo prieš konkurentus ir gerų klientų santykių palaikymo veiksnys.
Šiame straipsnyje siūlomas daugiakriterinis sprendimų priėmimo metodas (angl. MCDM), pagrįstas bipolinių
neutrosofinių skaičių ir Hemingo atstumo taikymu. Straipsnio tikslas yra pabrėžti tai, kad mažesnius kriterijus
turintys MCDM modeliai gali būti sudaromi taikant priešingus neutrosofinius skaičius ir dėl to nenukenčia
tikslumas. Be to, siūlomi trys variantai, skirti bipolinių neutrosofinių skaičių skaičiavimams pagal Hemingo
atstumą ir atstumą nuo idealaus taško. Siūlomo metodo taikomumas apžvelgiamas vertinant svetainę.
REIKŠMINIAI ŽODŽIAI: bipolinė neutrosofinė aibė, Hemingo atstumas, bendras, MCDM.
