An Intuitionistic Fuzzy Decision Aid for Neuromarketing Technology
Selection Problem
NAZLI GOKER, MEHTAP DURSUN
Industrial Engineering Department,
Galatasaray University,
Ciragan Street No. 36, Besiktas,
TURKEY
Abstract: - Neuromarketing, which uses neuroimaging technologies for marketing initiatives, is represented as
the application of neuroscientific methods for analysing and understanding consumer behaviour with regard to
marketing objectives. Medical diagnostic devices for brain imaging are used by marketers as neuromarketing
technologies. In this study, the intuitionistic fuzzy COPRAS method, which aims to obtain a solution relative to
the ideal solution, is used to rank neuromarketing technology alternatives and identify the best-performing one
among them. Intuitionistic fuzzy sets are used to deal with the loss of information and hesitation in data that
may occur in operations with fuzzy numbers. The application of the proposed intuitionistic fuzzy decision-
making approach is illustrated by conducting a case study.
Key-Words: - Neuromarketing technology selection, multi-criteria decision making, intuitionistic fuzzy
decision making, COPRAS
Received: April 11, 2022. Revised: April 19, 2023. Accepted: May 16, 2023. Published: July 5, 2023.
1 Introduction
Neuromarketing is utilized in various marketing
research areas namely product attraction, advertising
efficacy, brand awareness, brand loyalty, logo and
media selection. Coca-Cola, Delta, Estée Lauder,
Google, McDonald’s, Carlsberg Beer, Microsoft,
Procter & Gamble, and Yahoo are some of the
global firms that employ neuroscientific methods for
market research, [1]. Neuromarketing becomes
more and more widely used throughout the world
for two reasons. First, neuroimaging techniques may
be faster and less expensive than the other classical
marketing methods. Second, marketers can reach
classified information that is unavailable through
traditional marketing techniques. Another important
feature of neuromarketing is the fact that marketers
can utilize it before the product comes together with
customers. In other words, neuromarketing
techniques can be employed for early product
design, [2].
In order to employ neuromarketing methods,
companies utilize brain imaging techniques that can
be called “neuromarketing technologies” in this
work. Throughout the medical literature, there are a
lot of neuromarketing technologies namely fMRI
(functional magnetic resonance imaging), EEG
(electroencephalography), MEG
(magnetoencephalography), TMS (transcranial
magnetic stimulation), PET (positron emission
tomography), eye tracking, galvanic skin response,
electrocardiography, electromyography, analysis of
pupil dilation, blush, blinking, heartbeat, or
breathing, [2], [3]. fMRI, EEG, MEG, and TMS are
defined as medical diagnostic devices, which are
considered the most frequently used neuromarketing
technologies, [1]. fMRI, which is a technique using
an MRI scanner for measuring the blood
oxygenation level-dependent signal, is the most
widely used brain imaging technology in the world,
[1], [2]. EEG utilizes electrodes that are placed on
the head of a person to measure changes in the
electrical area of the brain region underneath, [2],
[4]. MEG, being an expensive version of EEG, is
applied to measure the changes in the magnetic area
induced by neuronal activity. TMS creates a
magnetic field for inducing electrical currents in
underlying neurons by using an iron core, which is
placed on one’s head, [2]. PET measures sensory
perception and valence of emotions as an invasive
method, [5]. These techniques have their own
strengths and limitations. Thus, the evaluation
should be conducted considering different criteria.
With its need to trade off multiple conflicting
criteria exhibiting vagueness and imprecision,
neuromarketing technology evaluation is a highly
important multi-criteria decision-making problem.
The classical multi-criteria decision-making
(MCDM) methods that consider deterministic or
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random processes cannot effectively address
decision problems including imprecise and
linguistic information. In practice, decision-making
in neuromarketing technology evaluation includes a
high degree of vagueness, imprecision, and also
hesitation.
In this study, the intuitionistic fuzzy COPRAS
(IFCOPRAS) method, which aims to obtain a
solution relative to the ideal solution, is used to rank
neuromarketing technology alternatives and identify
the best-performing one among them. Intuitionistic
fuzzy sets are used to deal with the loss of
information and hesitation in data that may occur in
operations with fuzzy numbers. The application of
the proposed intuitionistic fuzzy decision-making
approach is illustrated by conducting a case study by
collecting linguistic data from the experts. Four
neuromarketing technology alternatives are ranked,
and 7 evaluation criteria are utilized. The applied
decision approach provides including intuitionistic
fuzzy numbers in the decision framework for
expressing experts’ opinions, hence hesitation is
computed.
The rest of the study is organized as follows.
Section 2 outlines the IFCOPRAS method. Section
4 illustrates the application of the developed
methodology for the neuromarketing technology
evaluation problem. Finally, concluding remarks
and future research directions are delineated in the
last section.
2 Intuitionistic Fuzzy COPRAS
Method
Fuzzy set theory was initially presented by [6], to
cope with the decision problems that contain
uncertain and vague data. Fuzzy set theory has been
applied in various research studies that provide
applications in different sectors. It assumes that the
membership degree of an element is a single value
that is between zero and one. However, the non-
membership degree of an element may not always
be equal to one minus the membership degree due to
the hesitation degree, [7]. For that reason, [8],
proposed intuitionistic fuzzy sets (IFS), which
become the extension of fuzzy sets. IFS takes into
account the degree of hesitation that is computed as
one minus the sum of membership and non-
membership degrees.
The basic notions and some operations of IFS
are given as:
Definition 1, [9]. Let be a given set. An IFS
in E is an object Y described in
(1)
where
and
satisfy the
condition
for every
Hesitancy is equal to one minus the sum of
membership and non-membership degrees as
(2)
Definition 2, [10]. Let Y and Z be two IFSs in set E.
Namely,
and
The operations of summation and multiplication
between
and
are defined as
(3)
(4)
Definition 3, [10]. For any positive integer number
k,
is defined as
(5)
where
and
Definition 4, [11]. Let ,be an
intuitionistic fuzzy number. The score of is
defined as follows:
(6)
where
Definition 5, [12]. Let ,be an
intuitionistic fuzzy number. The normalized score of
is defined as
(7)
where
.
Decision problems in business life often require
numerous criteria, which are conflicted and related
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to each other. Besides, crisp numbers may not
always be available while collecting the data. In
such circumstances, fuzzy set theory is suitable to
cope with vagueness and imprecision in data. On the
other hand, fuzzy set theory fails to handle the
evaluation of membership and non-membership
because of the lack of information, and thus
hesitancy occurs. IFS theory is proposed to deal
with hesitation in decision processes. In this paper,
an integrated intuitionistic fuzzy decision aid
framework is introduced. The weighting process is
completed via the IFCM tool whereas the
IFCOPRAS method is employed for the selection
procedure. The COPRAS (Complex Proportional
Assessment) technique, which was initially
presented by [13], is an MCDM (multiple criteria
decision-making) method that determines a solution
relative to the ideal solution. The stepwise
illustration of the developed framework is as
Step 1. Form a committee of experts, identify the
alternatives (Ar=1,2,…,m), and the evaluation
criteria Ci (i=1,2,...,n).
Step 2. Obtain the data regarding the ratings of
alternatives according to the criteria, and the causal
relations among the criteria.
Step 3. Compute the importance weights of criteria
by following the steps of IFCM mentioned in
Section 3.2.
Step 4. Normalize the importance weights
employing Equation (8)
(8)
where represent the normalized weight of
criterion i.
Step 5. Start the selection process using the
IFCOPRAS method. Obtain weighted data using
Equation (9)
(9)
where represents the rating of the rth alternative
regarding ith criterion and is the weight of the ith
criterion, and
Step 6. Sum the cost and benefit criteria values.
Let be a set of cost criteria, i.e. the
minimum values refer to the superior option.
Calculate values for each alternative employing
Equation (10).
(10)
Step 7. Let be a set of
benefit criteria, i.e. the maximum values represent
superior choice. Calculate values for each
alternative employing Equation (11).
(11)
Step 8. Calculate the degree of relative weights of
alternatives using Equation (12), [14].
,
(12)
Step 9. Determine the priority of the alternatives
() using Equation (13) and rank the alternatives in
descending order.
=
(13)
3 Case Study
Neuromarketing, which makes use of neuroimaging
technologies for marketing goals, is employed in
many marketing research fields such as product
attraction, advertising efficacy, brand recognition,
fidelity to the brand, logo, and media selection.
Neuromarketing becomes more and more popular to
match products with consumers. In order to
illustrate the application of the proposed decision-
making method to the neuromarketing technology
selection problem, a case study conducted in a
marketing company located in Istanbul is
introduced. As a result of interviews with decision-
makers, four neuromarketing technologies that are
suitable for the company are identified as fMRI,
EEG, MEG, and TMS.
Determining the most appropriate
neuromarketing technology relies on a number of
distinct factors. Benefiting from the experts'
opinions and the literature, seven criteria relevant to
neuromarketing technology selection are defined as
equipment cost (€), spatial resolution (ms), temporal
resolution (ms), reliability, customer experience,
suitability, and willingness of participants.
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A committee of three decision-makers involving
a neuroscience researcher, a neurology specialist,
and a marketing specialist conducted the evaluation
process. A questionnaire is prepared regarding the
evaluation of alternatives with respect to qualitative
criteria. They created a consensus and used the
linguistic term set very low (VL), low (L), medium
(M), high (H), and very high (VH) as given in Table
1. Table 1. Linguistic scale
Linguistic variables
IFS
Very High (VH)
<0.95,0.05>
High (H)
<0.70,0.25>
Medium (M)
<0.50,0.40>
Low (L)
<0.25,0.70>
Very Low (VL)
<0.05,0.95>
The evaluation matrix of neuromarketing
technology alternatives is given in Table 2.
Table 2. Evaluation matrix
A1
A2
A3
A4
weight
C1
VH
VL
M
L
H
C2
VL
H
M
VH
M
C3
M
VL
VL
VL
M
C4
VH
M
H
M
VH
C5
L
VH
VL
L
L
C6
H
H
M
M
M
C7
M
M
L
VL
VL
Membership, non-membership, and hesitation
values are given in Table 3, Table 4, and Table 5,
respectively.
Table 3. Membership values
A1
A2
A3
A4
C1
0.95
0.05
0.5
0.25
C2
0.05
0.7
0.5
0.95
C3
0.5
0.05
0.05
0.05
C4
0.95
0.5
0.7
0.5
C5
0.25
0.95
0.05
0.25
C6
0.7
0.7
0.5
0.5
C7
0.5
0.5
0.25
0.05
Table 4. Non-membership values
A1
A2
A3
A4
C1
0.05
0.95
0.4
0.7
C2
0.95
0.25
0.4
0.05
C3
0.4
0.95
0.95
0.95
C4
0.05
0.4
0.25
0.4
C5
0.7
0.05
0.95
0.7
C6
0.25
0.25
0.4
0.4
C7
0.4
0.4
0.7
0.95
Table 5. Hesitation values
A1
A2
A3
A4
C1
0
0
0.1
0.05
C2
0
0.05
0.1
0
C3
0.1
0
0
0
C4
0
0.1
0.05
0.1
C5
0.05
0
0
0.05
C6
0.05
0.05
0.1
0.1
C7
0.1
0.1
0.05
0
After collecting intuitionistic fuzzy data, weighted
data are obtained using Definition (2) and given in
Table 6, Table 7, and Table 8, respectively.
Table 6. Membership values of weighted data
A1
A2
A3
A4
C1
0.665
0.035
0.35
0.175
C2
0.025
0.35
0.25
0.475
C3
0.25
0.025
0.025
0.025
C4
0.9025
0.475
0.665
0.475
C5
0.0625
0.2375
0.0125
0.0625
C6
0.35
0.35
0.25
0.25
C7
0.025
0.025
0.0125
0.0025
Table 7. Non-membership values of weighted data
A1
A2
A3
A4
C1
0.2875
0.9625
0.55
0.775
C2
0.97
0.55
0.64
0.43
C3
0.64
0.97
0.97
0.97
C4
0.0975
0.43
0.2875
0.43
C5
0.91
0.715
0.985
0.91
C6
0.55
0.55
0.64
0.64
C7
0.97
0.97
0.985
0.9975
Table 8. Hesitation values of weighted data
A1
A2
A3
A4
C1
0.05
0.0025
0.1
0.05
C2
0.05
0.1
0.11
0.095
C3
0.11
0.05
0.05
0.05
C4
0
0.095
0.05
0.095
C5
0.0025
0.0475
0.0025
0.0025
C6
0.1
0.1
0.11
0.11
C7
0.05
0.05
0.0025
0
The sum of cost and benefit criteria values are
calculated by employing Equations (10) and (11).
The degree of relative weights, as well as the
priorities of the alternatives, are computed using
Equations (12) and (13), and the alternatives are
ranked in descending order according to their
priorities. With respect to the results of the analysis,
EEG is identified as the most appropriate
alternative, which is followed by fMRI and MEG,
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respectively. Overall computational outcomes of the
IFCOPRAS methodology are given in Table 9.
Table 9. Overall computational outcomes
Rank
A1
0.788
0.947
1.401
0.871
2
A2
0.437
0.791
1.608
1
1
A3
0.591
0.788
1.392
0.865
3
A4
0.627
0.690
1.260
0.784
4
4 Conclusion
In this study, the IFCOPRAS method, which aims to
obtain a solution relative to the ideal solution, is
used to rank neuromarketing technology alternatives
and identify the best-performing one among them.
Intuitionistic fuzzy sets are used to deal with the
loss of information and hesitation in data that may
occur in operations with fuzzy numbers. The
application of the proposed intuitionistic fuzzy
decision-making approach is illustrated by
conducting a case study. Four neuromarketing
technology alternatives are proposed, and 7
evaluation criteria are utilized. The applied decision
approach provides including intuitionistic fuzzy
numbers in the decision framework for expressing
experts’ opinions, hence hesitation is computed.
Future research will focus on proposing a group
decision-making framework.
Acknowledgment:
This work is supported by Galatasaray University
Research Fund Project FBA-2022-1107.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Nazli Goker carried out COPRAS application.
Mehtap Dursun made interviews with the experts
and was responsible for redaction.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work is supported by Galatasaray University
Research Fund Project FBA-2022-1107.
Conflict of Interest
The authors declare that they have no conflict of
interest.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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