Fuzzy Sets Applied for Product Selection based on Customer

Preferences

Parapat Gultom

and Hardi Mulyono

Department of Mathematics, Universitas Sumatera Utara, Dr. Mansyur, Medan, Indonesia

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

𝑎

𝑎

; 𝑎

𝑥𝑎

𝑎

𝑥

𝑎

𝑎

; 𝑎

𝑥𝑎

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

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

: Tuition Fee Triangular [0,2,2,4]

: University Image Rectangular [2,2,8,8

: Facility Trapezoidal [1,3,6,8]

: Graduate Quality Triangular [2,5,5,8]

: 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

: Tuition Fee Trapezoidal [5,7,8,10]

: University Image Triangular [4,6,6,8]

: Facility Rectangular [4,4,8,8]

: Graduate Quality Triangular [1,3,3,5]

: 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

: Tuition Fee Trapezoidal [0,2,4,6]

: University Image Triangular [5,7,7,9]

: Facility Rectangular [4,4,7,7]

: Graduate Quality Triangular [4,6,6,8]

: 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

: Tuition Fee Trapezoidal [5,6,8,9]

: University Image Triangular [0,3,3,6]

: Facility Trapezoidal [1,4,8,10]

: Graduate Quality Rectangular [4,4,9,9]

: 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

)

: Tuition Fee LI I M

: University Image HI HI I

: Facility M LI I

: Graduate Quality HI I HI

: Research Quality I M HI

Note:

HI (Highly Important), I (Important), M (Medium), LI

(Low Important), NI (Not Important)

012345678910

MNI

012345678910

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

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and Manufacturing.

Hanif, M., Hafeez, S., & Riaz, A. (2010). Factors

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Jamali, D. (2007). A study of customer satisfaction in the

context of a public private partnership. International

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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.

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Production Research.

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