Fuzzy clustering based on linguistic information: a case study on clustering destinations with tourists’ perceptions

• Author: Chao‐Qun Ma,Wu‐E Yang,Zhi‐Qiu Han,Ying‐Ming Wang
• Published date: 01 May 2020
• Date: 01 May 2020
• DOI: http://doi.org/10.1111/itor.12721

Intl. Trans. in Op. Res. 27 (2020) 1526–1549

DOI: 10.1111/itor.12721

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

Fuzzy clustering based on linguistic information: a case study

on clustering destinations with tourists’ perceptions

Zhi-Qiu Hana,b, Wu-E Yanga,∗, Ying-Ming Wangb,c and Chao-Qun Mad

aSchool of Economics & Management, Fuzhou University, Fuzhou, Fujian 350116, China

bDecision Sciences Institute, Fuzhou University, Fuzhou 350116, China

cKey Laboratory of Spatial Data Mining & InformationSharing of Ministry of Education, Fuzhou University, Fuzhou

350116, China

dSchool of Business Administration, Hunan University, Changsha 410082, China

E-mail: hanzhiqiu@fzu.edu.cn [Han]; yangwue@gmail.com [Yang]; msymwang@hotmail.com[Wang];

cqma1998@126.com [Ma]

Received 7 October 2018; receivedin revised form 18 April 2019; accepted 26 August 2019

Abstract

A fuzzy clustering method with linguistic information is introduced.It uses a minimizing cross-entropy model

to avoid setting the clustering threshold artificially. During the clustering, the semantics of the linguistic

information is conservatively represented by solving a programming. It maximizes the potential differences

between the objects to be clustered, and further helps an analyst to reach a semantics-robustclustering result.

A case study on clustering a sample destination set, which includes 13 Asia Pacific regions, based on a group

of tourists’ perceptions is also proposed.

Keywords:multicriteria; linguistic modeling; fuzzy relation; cross-entropy; tourism management

1. Introduction

Clustering is oriented to identify similarities among objects and then group them based on several

criteria (Loudon and Della Bitta, 1993; Hair et al., 2009; Kaufman and Rousseeuw, 2009). In all

the clustering methods, the fuzzy clustering models have the advantage to incorporate the uncertain

data (Saha et al., 2019). Thereby, they are prevalent in the literature (Hidri et al., 2018; Dagher,

2018; Binesh and Rezghi, 2018; Bai et al., 2018b).

Generally, the existing fuzzy clustering methods can be grouped into two types, namely nonhier-

archical and hierarchical clustering:

(1) Nonhierarchical methods such as fuzzy K-means algorithms (Bai et al., 2018a; Zhang et al.,

2019) need aprioridefinition of the number of classes (called clusters). The final clustering result

∗Corresponding author.

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Z.-Q. Han et al. / Intl. Trans.in Op. Res. 27 (2020) 1526–1549 1527

a1a2a3a4a5

2 clusters

Fig. 1. Clustering with apriorideter mined cluster number.

a1 a2 a3 a4 a5

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

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Fig. 2. Hierarchical clustering map with dynamicparameter λ.

highly depends on this number. Figure 1 gives an illustration of this type of clustering, which

aprioridefined the cluster number as 2. If given another cluster number, the clustering result

changes accordingly.

(2) Hierarchical methods are based on fuzzy relations (Klir and Yuan, 1995; Xie and Liu, 2006),

which avoid any aprioriassumption on the number of clusters. It has the merit to extract

unbiased results that reflect the structure of the given data. Its results usually can be visually

presented by a clustering map with dynamic parameter λ(Fig. 2). But when a unique clustering

result is required in practice, such dynamic procedure will trouble an inexperienced user in

choosing an appropriate clustering parameter.

If we can overcome the difficulty in choosing the clustering parameter, these methods will be

more attractive and useful. For solving this problem in the hierarchical framework, we introduce a

mechanical procedure to find the optimal clustering parameter based on minimizing cross-entropy

principle (Kullback, 1959).

Additionally, in many real clustering problems, the evaluations of objects with respect to criteria

are usually collected by questionnaires, which profile or measure the preference of respondents

by ranking scales (LaMondia et al., 2010). But the inherent vagueness in human cognition makes

it difficult to be valued with crisp numbers in practice. While using the Likert scale (Jamieson,

2004) to evaluate the preference, the meaning of the scale values is perhaps not so clear for using

appropriately. Thereby,to facilitate the gathering of the preference information with questionnaires,

we can use linguistic variables.

The linguistic variables are words or sentences in a natural or artificial language (Zadeh, 1975).

Their values are often taken from a set of linguistic terms. These terms are usually arranged as a

linguistic ordered scale (Chiclana et al., 2000). It has been increasingly used to measure qualitative

factors in investigations, especially in social science research (Ding et al., 2017; Liern and Perez-

Gladish, 2018; Wang et al., 2018; Shiu et al., 2019). Compared to the Likert scale, the linguistic

ordered scale is more expressivein practice because it has absolutely meaningful landmarks (Dubois,

2011; Xia and Xu, 2018).

For operating and integrating the linguistic information, the semantics of linguistic variables are

required to be represented by some symbolic or mathematical materials. Such representation is

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2019 The Authors.

International Transactionsin Operational Research C

2019 International Federation of OperationalResearch Societies