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WEB CONFERENCING SOFTWARE SELECTION
WITH INTERVAL-VALUED FUZZY PARAMETERIZED
INTUITIONISTIC FUZZY SOFT SETS
Esra Çakır
Department of Industrial Engineering, Galatasaray University, Istanbul, (Turkey).
E-mail: ecakir@gsu.edu.tr
ORCID: https://orcid.org/0000-0003-4134-7679
Ziya Ulukan
Department of Industrial Engineering, Galatasaray University, Istanbul, (Turkey).
E-mail: zulukan@gsu.edu.tr
ORCID: https://orcid.org/ 0000-0003-4805-2726
Recepción:
03/12/2020
Aceptación:
18/02/2021
Publicación:
07/05/2021
Citación sugerida:
Çakır, E., y Ulukan, Z. (2021). Web Conferencing Software Selection with Interval-Valued Fuzzy
Parameterized Intuitionistic Fuzzy Soft Sets. 3C Tecnología. Glosas de innovación aplicadas a la pyme, Edición
Especial, (mayo 2021), 53-65. https://doi.org/10.17993/3ctecno.2021.specialissue7.53-65
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ABSTRACT
Since COVID-19 has become a pandemic, education has been interrupted in many
countries, and training has been temporarily resumed on online platforms. But it is dicult
to determine which of the many existing web (or video) conferencing software is more
suitable for class education. The aim of this study is to sort these platforms according to
the criteria determined by experts and select the best one among dierent alternatives by
using interval-valued fuzzy parameterized intuitionistic fuzzy soft sets. In the application,
seven experts determined the six criteria and their interval-valued fuzzy weights depending
on educational needs. The decision makers are evaluated ten video conferencing tools for
educational institutions by using interval-valued fuzzy parameterized intuitionistic fuzzy
soft sets. Finally, using the proper operators, the alternatives are sorted and the best video
conferencing tool for class education. The results are intended to guide future research.
KEYWORDS
Fuzzy MCDM, Interval-valued fuzzy sets, Intuitionistic fuzzy soft sets, Web conferencing
tool, Software selection.
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1. INTRODUCTION
Due to the Covid-19 epidemic, countries had to take a break from education for a while and
sought new ways to continue. After curfews came in many countries, educational institutions
started looking for a suitable online video conferencing platform. These software allow
participants to conduct or attend meetings via the internet. They enable remote meetings
based on VoIP, online video, instant messaging, le sharing, and screen sharing. Online
video conferencing is fundamental to many organizations conduct business in recent years.
However, it has also become a must for formal education since the announcement of the
pandemic.
Web conferencing software includes presentations or webinars, conference calls, video
meetings with multiple participants, running product demos and training, one-on-one
meetings with remote employees and face-to-face customer support. They are also useful
in enhancing communications, reducing travel costs and increasing eciency (Grant &
Cheon, 2007; Roehrs, 2013). By synchronous web conference communication, the gap
between digital technologies and face-to-face teaching can be lled and this also encourages
students to be attracted toward learning and in support of their self-working (Nedeva,
Dineva & Atanasov, 2014).
In order to adapt these platforms, which are very advantageous in the period when they
are obliged to distance education, to their systems quickly and reliably, institutions should
make decisions according to some criteria. Therefore, it is necessary to use expert opinions
to select them and uncertainties views must also be considered. The fuzzy set proposed
by Zadeh (1965) and improved by Atanassov (1986) as intuitionistic fuzzy sets are suitable
for this application. Also, interval valued fuzzy sets (Atanassov & Gargov, 1989) and
intuitionistic fuzzy soft sets (Molodtsov, 1999) can sort alternatives and the robustness of
their combined version has been proven (Nedeva et al., 2014). Jiang et al. (2010) proposed
the notion of the interval-valued intuitionistic fuzzy soft set theory. It is an interval-valued
fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension
of the interval-valued fuzzy soft set theory. The basic properties of the interval-valued
intuitionistic fuzzy soft sets are also presented in their study. Deli and Karataş (2016) dened
interval-valued intuitionistic fuzzy parameterized soft sets by combining the interval-valued
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intuitionistic fuzzy sets and the soft sets from parametrization point of view. By using soft
level sets, they construct a parameter reduction method. Tripathy and Panigrahi (2016)
extend hybrid model of interval valued fuzzy set and soft set to dene interval valued
intuitionistic fuzzy parameterized soft set (IVIFPSS) and establish their properties. They
put forth two algorithms in decision-making. Aydın and Enginoğlu (2020) proposed the
concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic
fuzzy soft sets (d-sets) and presents several of its basic properties. By using d-sets, they suggest
a new soft decision-making method and apply it to a problem concerning the eligibility of
candidates for two vacant positions in an online job advertisement.
The contribution of this study to the existing literature is to sort web conferencing platforms
according to the criteria determined by experts and select the best one among ten options
by using interval valued fuzzy parameterized intuitionistic fuzzy soft sets.
The rest of the article is organized as follows. Section 2 examines preliminaries and ranking
methodology of interval valued fuzzy parameterized intuitionistic fuzzy soft sets. Section 3
presents numerical application in the selection of web conferencing tool. Conclusion of the
study are stated in Section 4, along with future research.
2. METHODOLOGY
In this section, the preliminaries and denitions of the interval valued fuzzy parameterized
intuitionistic fuzzy soft sets (IVFPIFS) and aggregation operator are introduced. The steps
of methodology are given at the end of the section.
2.1. PRELIMINARIES
Denition 1. (Atanassov & Gargov, 1989) Let A be a collection of objects (points) denoted
by α
1
. Also, let ([0,1]) be the set of all closed subintervals of the interval [0,1]. Then, an
interval-valued intuitionistic fuzzy set (IVIFS) Z in A is dened as
(1)
where ([0,1]) are respectively called the
membership function and the non-membership function of Z with property
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and . The values and denote the lower and
upper degrees of membership of the element and also the values and
denote the lower and upper degrees of non-membership of the element , respectively.
Note that
and notations can be use instead of and for .
Denition 2. (Atanassov & Gargov, 1989) Let
and
be two IVIF values. Then, the operations and for γ
1
and
γ
2
are respectively dened as follows:
(2)
(3)
Denition 3. (Tan, 2011; Xu, 2010) Let
be the
IVIF value of
. Then, the score function and accuracy function of γ
1
are respectively
dened as follows:
(4)
(5)
To compare two IVIF values γ
1
and γ
2
, a ranking method is dened as follows:
Denition 4. Let U be a universal set and C be the set of parameters. Also, let I be an
interval-valued fuzzy set over C with the membership function ω
1
:C Int([0,1]). Then, an
interval-valued fuzzy parameterized intuitionistic fuzzy soft set (IVFPIFS set)
on U is a
set of ordered pairs
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(6)
where the function
such that
. Note that IVFPIF(U) notation denotes the set of all interval-
valued fuzzy parameterized intuitionistic fuzzy soft sets on U.
Denition 5. Let
be an IVFPIFS set,where
indicates an intuitionistic fuzzy value when the alternative
α
1
is assessed with respect to the parameter c
j
and indicates an
interval-valued fuzzy value of the parameter c
j
. Then,
• the rst IVFPIFS-aggregation operator, denoted by
, is dened by
(7)
where
which is an interval-valued intuitionistic
fuzzy set on U. The membership degree
and the non-membership degree
of is dened as follows:
(8)
(9)
where m denotes the number of parameters in C.
• the second IVFPIFS-aggregation operator, denoted by
, is dened by
(10)
where
which is an interval-valued intuitionistic
fuzzy set on U. The membership degree
and the non-membership degree
of is dened as follows:
(11)
(12)
where m denotes the number of parameters in C.
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2.2. ALGORITHM
This methodology is stated for multi criteria decision making problem. It uses interval
valued fuzzy parameterized intuitionistic fuzzy soft sets to express decision makers opinion
and generate interval valued intuitionistic fuzzy sets by using two dierent aggregation
operators (Nedeva et al., 2014). Score and accuracy functions help to sort the alternatives
and to select best option. The steps of this methodology are as follows:
• Step 1: Set the problem. α
1
indicates alternative i.
• Step 2: Select experts and determine criteria with weights by experts. C
j
indicates
criterion j and its interval-valued fuzzy weight is expressed as
.
• Step 3: Collect the fuzzy decision matrices with IVFPIFS set by experts and
aggregate them by fuzzy geometric mean method of Buckley (Buckley, 1985).
• Step 4: Obtain the rst and second aggregate interval-valued intuitionistic fuzzy
set
and of alternatives by using IVFPIFS-aggregation
operators given in Def. 5.
• Step 5: Calculate the IVIF values
of alternatives by applying
operation given in Def. 2.
• Step 6: By using the score function and accuracy function on IVIF values given in
Def. 3, compare the alternatives and set the highest score alternative as the best
option.
3. APPLICATION
After being declared COVID-19 pandemic, educational institutions in many countries took
a break for a while. In order not to fall behind in education, many institutions have evaluated
opportunities for distance education. With the web (or video) conferencing software, teachers
had the chance to teach their classes during the periods they set. However, these systems
had to be selected and adapted to the institutions in a very short time. So, it is a problem
to determine which service is better. In this application, the alternatives are evaluated, and
the criteria are determined with the help of experts in Turkey. Platforms are ranked using
interval valued fuzzy parameterized intuitionistic fuzzy soft sets, and the alternative with
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the highest score is evaluated as the best platform. According to the previous section, this
application is implemented step by step as follows:
• Step 1: Web conferencing software used in Turkey selection is set as the problem.
The ten most frequently used software during the pandemic period are determined
as alternatives. The alternatives are presented as A={α
1
, α
2
, α
3
, α
4
, α
5
, α
6
, α
7
, α
8
, α
9
,
α
10
}.
• Step 2: Seven experts are selected, and they determined the criteria depending on
educational needs and the features of tools. These criteria are given with their
interval-valued fuzzy weights in Table 1.
Table 1. The criteria for web conferencing software selection with their interval-valued fuzzy weights.
Criteria code Criteria Interval-valued fuzzy weights "ω
i
"
c
1
Performance and Compatibility [0.6, 0.9]
c
2
File and Screen Sharing [0.3, 0.5]
c
3
Online Meeting Quality and Recording [0.6, 0.8]
c
4
Implementation [0.4, 0.7]
c
5
Security [0.7, 0.9]
c
6
Support System [0.5, 0.8]
Source: own elaboration.
• Step 3: Experts decided on the degree of membership of alternatives to specied
criteria with IVFPIFS set expressions and their decision matrices are aggregated
by fuzzy geometric mean method of Buckley. The aggregated decision matrix is
represented in Table 2.
Table 2. The aggregated IVFPIFS decision matrix.
Crt.
Alt.
c
1
c
2
c
3
c
4
c
5
c
6
ω
1
= [0.6,0.9] ω
2
= [0.3,0.5] ω
3
= [0.6,0.8] ω
4
= [0.4,0.7] ω
5
= [0.7,0.9] ω
6
= [0.5,0.8]
α
1
<0.72, 0.22> <0.68, 0.21> <0.86, 0.12> <0.67, 0.22> <0.67, 0.21> <0.63, 0.36>
α
2
<0.71, 0.19> <0.66, 0.33> <0.83, 0.11> <0.32, 0.51> <0.63, 0.18> <0.51, 0.48>
α
3
<0.63, 0.31> <0.62, 0.15> <0.73, 0.23> <0.51, 0.38> <0.65, 0.25> <0.49, 0.51>
α
4
<0.65, 0.33> <0.6, 0.38> <0.82, 0.1> <0.59, 0.24> <0.6, 0.22> <0.48, 0.4>
α
5
<0.68, 0.29> <0.63, 0.27> <0.82, 0.05> <0.65, 0.22> <0.63, 0.2> <0.54, 0.37>
α
6
<0.65, 0.23> <0.67, 0.33> <0.78, 0.22> <0.49, 0.36> <0.63, 0.14> <0.4, 0.55>
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α
7
<0.68, 0.17> <0.62, 0.3> <0.77, 0.09> <0.62, 0.23> <0.59, 0.31> <0.55, 0.42>
α
8
<0.66, 0.24> <0.63, 0.29> <0.73, 0.14> <0.66, 0.21> <0.65, 0.24> <0.55, 0.36>
α
9
<0.59, 0.4> <0.45, 0.46> <0.69, 0.15> <0.52, 0.31> <0.54, 0.28> <0.34, 0.58>
α
10
<0.62, 0.26> <0.56, 0.41> <0.74, 0.22> <0.48, 0.36> <0.5, 0.31> <0.63, 0.33>
Source: own elaboration.
• Step 4: The rst and second aggregate interval-valued intuitionistic fuzzy set
and of alternatives by using IVFPIFS-aggregation operators
are obtained as in Table 3.
Table 3. The aggregate interval-valued intuitionistic fuzzy sets of alternatives.
Alt.
α
1
<[0.94173, 0.99242], [0.0000013, 0.0000167]> <[0.0018, 0.021605], [0.518534, 0.683016]>
α
2
<[0.91607, 0.98383], [0.0000045, 0.0000551]> <[0.000604, 0.007255], [0.605775, 0.79045]>
α
3
<[0.906801, 0.97983], [0.0000078, 0.000094]> <[0.0007003, 0.008403], [0.65074, 0.81673]>
α
4
<[0.914425, 0.983378], [0.000004, 0.000048]> <[0.000821, 0.009859], [0.59133, 0.762296]>
α
5
<[0.92635, 0.98774], [0.0000009, 0.0000115]> <[0.001174, 0.014094], [0.52932, 0.700298]>
α
6
<[0.90677, 0.97992], [0.0000069, 0.0000839]> <[0.000634, 0.007610], [0.62262, 0.800249]>
α
7
<[0.917029, 0.98471], [0.000002, 0.0000249]> <[0.000987, 0.01185], [0.565806, 0.731641]>
α
8
<[0.91994, 0.98553], [0.0000026, 0.0000320]> <[0.001082, 0.012994], [0.55262, 0.716573]>
α
9
<[0.86611, 0.961247], [0.000021, 0.0002521]> <[0.000264, 0.003173], [0.70188, 0.863861]>
α
10
<[0.895486, 0.97648], [0.000013, 0.0001567]> <[0.000587, 0.00704], [0.640429, 0.800823]>
Source: own elaboration.
• Step 5: The IVIF values of alternatives by applying operation is
calculated as in Table 4.
• Step 6: The scores and accuracy values of IVIF values are presented in Table 5.
Table 4. The interval valued intuitionistic fuzzy values of alternatives.
Alt.
α
1
<[0.94184, 0.992584], [0.000000722, 0.0000114]>
α
2
<[0.916128, 0.983951], [0.00000278,784538, 0.0000435]>
α
3
<[0.906867, 0.9800047], [0.00000509,652078, 0.0000767]>
α
4
<[0.914496, 0.983541], [0.00000236,637966, 0.0000366]>
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α
5
<[0.926436, 0.987917], [0.00000051,809846133,180987]>
α
6
<[0.906831, 0.980079], [0.000004357,035645, 0.0000672]>
α
7
<[0.917111, 0.984898], [0.00000117,284747, 0.0000182]>
α
8
<[0.920028, 0.985722], [0.00000147,515918, 0.0000229]>
α
9
<[0.866147, 0.96137008], [0.0000147, 0.0002177]>
α
10
<[0.8955477, 0.9766463], [0.00000836,714534, 0.0001254]>
Source: own elaboration.
Table 5. The scores of alternatives.
Alternative
Score s(
α
1
) Accuracy a(α
1
)
α
1
-0.02538 0.967219
α
2
-0.03393 0.950064
α
3
-0.0366 0.943477
α
4
-0.03454 0.949039
α
5
-0.03074 0.957181
α
6
-0.03666 0.943491
α
7
-0.0339 0.951015
α
8
-0.03286 0.952888
α
9
-0.04771 0.913875
α
10
-0.04061 0.936164
Source: own elaboration.
According to the scores, the ranking of the alternatives is α
1
>α
5
>α
8
>α
7
>α
2
>α
4
>α
3
>α
6
>α
10
>α
9
. Since α
1
has the highest score, it is selected as the best option for education institutions
based on determined criteria and expert’s opinions.
4. CONCLUSIONS
Due to the COVID-19 outbreak, interest in web conferencing platforms has increased in
educational institutions around the world. Since there are many dierent options, which
software institutions choose is an important issue. The aim of this study is to compare
ten video conferencing software according to the criteria determined by the experts with
their imprecise opinions and to choose the best option by using interval valued fuzzy
parameterized intuitionistic fuzzy soft sets. As a result of the study, alternatives are listed as
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α
1
>α
5
>α
8
>α
7
>α
2
>α
4
>α
3
>α
6
>α
10
>α
9
and “α
1
” platform is chosen as the best video conferencing
tool for educational institutions according to the determined criteria.
5. ACKNOWLEDGEMENTS
This work has been supported by the Scientic Research Projects Commission of
Galatasaray University under grant number # FBA-2020-1036.
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