Fuzzy Sets Applied for Product Selection based on Customer
Preferences
Parapat Gultom
1
and Hardi Mulyono
2
1
Department of Mathematics, Universitas Sumatera Utara, Dr. Mansyur, Medan, Indonesia
2
University of Muslim Nusantara Al Washliyah, Medan, Indonesia
Keywords: Fuzzy Sets, Product Selection, Customer Preferences.
Abstract: Selection process to decide purchasing of a product is a very important process especially on the increasing
of competitiveness among products. Many factors are put into consideration such as packaging, reliability,
appearance, after sales price, facility, accessories, and so on. Consumer ratings of each of these factors are
different ant it is stated as customer’s preference. Mostly customer’s preferences are stated in linguistic
terms, for solving this conditions, fuzzy sets can be applied. The solutions of such a problem is discussed in
this paper. An illustrative example, selection of university by candidate students, is presented to show how
the problems can be solved using fuzzy sets approach. The results showed that difference preferences on the
attributes of the university will yield different decision of the university selected.
1 INTRODUCTION
Product selection is a part of customer satisfaction.
A customer tries to select the best product which is
reflected by many attributes such as quality of a
product, price of product, availability of the product,
and the variety of a product. Indeed, customer
satisfaction can be measured by the customer's
response to the fulfillment of the suitability of the
expected preferences (Kim et al., 2004). Consumers
must choose products from so many products
available based on the proximity of the desired
preferences. Thus, the customer satisfaction can be
reflected based on the level of preference achieved.
On product selection, a customer provides
preferences on each attribute which are regularly
expressed in a cryptic, relative, and generally
expressed in linguistic terms. In this condition,
various fuzzy techniques can be applied.
2 LITERATURE REVIEW
Research on fuzzy satisfaction has been conducted
by many researchers. Using the analytical hierarchy
process and fuzzy set theory, Liu (1995) in his paper
focus on customer satisfaction. Whilst, Kuo (1996),
in order to measure customer’s satisfaction level by
applied a fuzzy neural network in general with a
back propagation learning model.
There are many membership function can be
applied to solve information in linguistic terms, such
as the triangular membership function, rectangular
membership function, and trapezoidal membership
function. Among all, the one of the most frequently
used is triangular membership function as shown in
the following Figure 1.
Figure 1: Triangular Fuzzy Number.
where,
𝜇



𝑥


⎩
⎪
⎨
⎪
⎧
𝑥𝑎
1
𝑎
2
𝑎
1
; 𝑎
1
𝑥𝑎
2
𝑎
3
𝑥
𝑎
3
𝑎
2
; 𝑎
2
𝑥𝑎
3
0 ; others
456
Gultom, P. and Mulyono, H.
Fuzzy Sets Applied for Product Selection based on Customer Preferences.
DOI: 10.5220/0010204700002775
In Proceedings of the 1st International MIPAnet Conference on Science and Mathematics (IMC-SciMath 2019), pages 456-459
ISBN: 978-989-758-556-2
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Hanif et al. (2010) mentioned factors affecting
customer satisfaction. While Jamali (2007)
focused on customer satisfaction at a public
private partnership. In fuzzy area, Wang (1997)
applied fuzzy outranking method for conceptual
design evaluation.
3 FUZZY SETS APPLIED
To solve the problem of product selection where
costumer’s preferences are stated in linguistic terms,
Barajas & Agard (2011) can be applied with the
following steps.
Step 1: Identify the market and technical evaluation
of products
Step 2: Prioritize the general features
Step 3: Consider customer’s preference
Step 4: Select the product
Barajas & Agard (2011) proposed a method to
evaluate the features that are the best and closest to
the customer’s preferences. Furthermore, based on
the definition of standard deviation, they proposed a
Fuzzy Indifference Degree (FID) with the best
choice corresponds to the smallest FID of the set of
products at issue. The following equation is a way to
measure of the degree of indifference between the
product features and the customer preferences:
𝐹𝐼𝐷



∑

𝑅
𝐴

,𝐵

0.5




𝑚1
(1)
where:
𝑅𝐴

,𝐵

 is a notation about the fuzzy preference
relation between 𝐴

and 𝐵

The set 𝐴



𝑎

,𝑎

,…,𝑎


is features

𝑗

for
product

𝑖

for all 𝑖1,2,…,𝑛 and for all 𝑗
1,2,…,𝑚, and
𝐵

𝑏

,𝑏

,…,𝑏

 is the set of features 𝑗 for
customer 𝑘 for all 𝑗1,2,…,𝑚 and for all 𝑘
1,2,…,𝑝.
𝑚 is the number of attributes.
Then, the following expression is the best product
𝑖 for customer 𝑘 is determined by applying
equation 1:
𝐵𝑃

min

𝐹𝐼𝐷

,𝐹𝐼𝐷

,…,𝐹𝐼𝐷


(2)
where 𝐵𝑃

is the best product alternative for
customer 𝑘.
To calculate the indifference between fuzzy
numbers is as follows:
Let A and B be two fuzzy numbers with convex and
normal properties. In this case, there are two
possibilities, i.e. the indifference and the dominance
between them. The indifference area is an area of
overlap between fuzzy numbers A and B
(intersection between A and B), as depicted in
Figure 2.
Figure 2: Dominance and indifference between A and B.
To calculate the non-overlap areas, it is used the
Hamming distance as follows:
𝐷

𝐴
,𝐵
|
𝑆  
|
𝜇


𝑢

 𝜇


𝑢
|
𝑑𝑢

∈

(3)
𝑆𝔎,𝐷

𝐴
,𝐵
|
𝔎𝐷 
𝐴
,𝐵 (4)
4 AN ILUSTRATIVE EXAMPLE
In selection of university, a candidate student
decides five attributes to be considered including
tuition fee, university image, facility, graduate
quality, and research quality. There are four
universities can be selected by a candidate student,
i.e. University A, B, C, and D. There are three
candidate students to select the best universities for
them.
4.1 The Evaluation of University’s
Attributes
The attribute’s values for each university are shown
in Table 1-4 and Figure 3-6.
Table 1: Attribute’s Value for University “A”.
Attribute Fuzzy Number Value
A
1
: Tuition Fee Triangular [0,2,2,4]
A
2
: University Image Rectangular [2,2,8,8
A
3
: Facility Trapezoidal [1,3,6,8]
A
4
: Graduate Quality Triangular [2,5,5,8]
A
5
: Research Quality Trapezoidal [3,6,9,10]
Fuzzy Sets Applied for Product Selection based on Customer Preferences
457

Figure 3: Attribute’s Value for University “A”.
Table 2: Attribute’s Value for University “B”.
Attribute Fuzzy Number Value
A
1
: Tuition Fee Trapezoidal [5,7,8,10]
A
2
: University Image Triangular [4,6,6,8]
A
3
: Facility Rectangular [4,4,8,8]
A
4
: Graduate Quality Triangular [1,3,3,5]
A
5
: Research Quality Trapezoidal [0,2,5,6]
Figure 4: Attribute’s Value for University “B”.
Table 3: Attribute’s Value for University “C”.
Attribute Fuzzy Number Value
A
1
: Tuition Fee Trapezoidal [0,2,4,6]
A
2
: University Image Triangular [5,7,7,9]
A
3
: Facility Rectangular [4,4,7,7]
A
4
: Graduate Quality Triangular [4,6,6,8]
A
5
: Research Quality Triangular [2,5,5,6]
Figure 5: Attribute’s Value for University “C”.
Table 4: Attribute’s Value for University “D”.
Attribute Fuzzy Number Value
A
1
: Tuition Fee Trapezoidal [5,6,8,9]
A
2
: University Image Triangular [0,3,3,6]
A
3
: Facility Trapezoidal [1,4,8,10]
A
4
: Graduate Quality Rectangular [4,4,9,9]
A
5
: Research Quality Triangular [3,5,5,7]
Figure 6: Attribute’s Value for University “D”.
4.2 General Prioritization of Attributes
Prioritization of attributes, it is assumed as depicted
in Figure 7.
Figure 7: Definition of General Attribute Prioritization.
Based on Figure 7, five different levels are defined in
linguistic terms as follows:
 HI reflects “highly important” and it indicates with [6 9
10 10],
 I reflects “important” and it indicates with [5 6 8 9],
 M reflects “a medium importance” and it indicates with
[4 5 5 6],
 LI reflects s “of low importance” and it indicates with [1
2 4 5],
 NI reflects “not important” and it indicates with [0 0 1 4].
4.3 Consideration of Customer’s
Preference
There are three candidate students who have
different preference on each attribute as shown in
Table 5.
Table 5: Candidate Student’s Preferences on Attribute
Attribute Attribute preferences for
Candidate Student (C
k
)
C
1
C
2
C
3
A
1
: Tuition Fee LI I M
A
2
: University Image HI HI I
A
3
: Facility M LI I
A
4
: Graduate Quality HI I HI
A
5
: Research Quality I M HI
Note:
HI (Highly Important), I (Important), M (Medium), LI
(Low Important), NI (Not Important)
012345678910
μ
1
I
MNI
LI
u
HI
012345678910
1
A4
A3
A2
A1
μ
u
A5
012345678910
μ
1
A4
A3
A2
A1
u
A5
012345678910
μ
1
A4
A3
A2
A1
u
A5
012345678910
μ
1
A4
A3
A2
A1
u
A5
IMC-SciMath 2019 - The International MIPAnet Conference on Science and Mathematics (IMC-SciMath)
458

Table 5 presents a candidate student’s feature
preferences. It shows, candidate student 1 states that
university image and graduate quality are highly
important attributes, research quality is important,
facility is an attribute with a medium level of
preference, and tuition fee is an attribute with low
importance. For candidate student 2, university
image is a highly important attribute, tuition fee and
graduate quality are two important attributes,
research quality is also an attribute with a medium
level of preference, and facility is an attribute of low
importance. For candidate student 3, both graduate
quality and research quality are highly important
attributes, university image and facility are
important, and tuition fee is a medium level of
preference.
4.4 University Selection Procedure
The process of university selection is started to
attain the relation of fuzzy preference between
university’s features and candidate student’s
preferences.
By using equation 1), Fuzzy Indifference Degree
(FID) for each university and a candidate student
can be calculated as presented in Tables 6, 7, and 8.
Table 6: Fuzzy Indifference Degree per University for
Candidate Student 1.
University Fuzzy Indifference Degree (FID)
A 0.4032
B 0.4426
C 0.2876
D 0.4143
Table 7: Fuzzy Indifference Degree per University for
Candidate Student 2.
University Fuzzy Indifference Degree (FID)
A 0.4532
B 0.2134
C 0.4876
D 0.4253
Table 8: Fuzzy Indifference Degree per University for
Candidate Student 3.
University Fuzzy Indifference Degree (FID)
A 0.2182
B 0.4486
C 0.4367
D 0.4643
Based on the results in Table 6-8, then the best
selection for each candidate student as shown in
Table 9.
Table 9: Best Selection for Each Candidate Student.
Candidate Student Best University Alternative
C1 C
C2 B
C3 A
5 CONCLUSION
Selecting best product by a customer involves many
attributes to be considered. Preferences for each
attribute that decides by a customer in some cases
are stated in linguistic terms. This paper covers the
fuzzy set to be applied to solve such problems, and it
is applied on university selection by a candidate
student. The Fuzzy Indifference Degree (FID) was
proposed to find the best choice for a customer
based on his/her preferences. The best choice
provides the good values for each attribute of the
product.
REFERENCES
Barajas, M., & Agard, B. (2011). Selection of Products
Based On Customer Preferences Applying Fuzzy
Logic. International Journal for Interactive Design
and Manufacturing.
Hanif, M., Hafeez, S., & Riaz, A. (2010). Factors
Affecting Customer Satisfaction. International
Research Journal of Finance and Economics, 60.
Jamali, D. (2007). A study of customer satisfaction in the
context of a public private partnership. International
Journal of Quality and Reliability Management, 24(4).
Kim, M. K., Park, M. C., & Jeong, D. H. (2004). The
effects of customer satisfaction and switching barrier
on customer loyalty in Korean mobile
telecommunication services.
Kuo, Y.-F. (1996). An artificial fuzzy neural controller
and its application to customer satisfaction
measuremen. The University of Texas.
Liu, M.-T. (1995). Fuzzy models for industrial
performance and customer satisfaction. The
University of Texas.
Wang, J. (1997). A fuzzy outranking method for
conceptual design evaluation. International Journal of
Production Research.
Fuzzy Sets Applied for Product Selection based on Customer Preferences
459