Managing information measures for hesitant fuzzy linguistic term sets and their applications in designing clustering algorithms

• Published in: Information fusion 2019-10, Vol.50, p.30-42
• Main Authors: Tang, Ming, Liao, Huchang
• Format: Article
• Language: English
• Subjects: Clustering algorithm; Hesitant fuzzy linguistic term set; Inclusion measure; Information measure; Water resource bearing capacity
• ISSN: 1566-2535; 1872-6305
• DOI: 10.1016/j.inffus.2018.10.002

•The concept of inclusion measure for HFLTS is defined.•The relationships among distance measure, similarity measure, entropy measure, inclusion measure of HFLTS are discussed.•The clustering algorithms based on correlation measure and distance measure are proposed.•The clustering algorithms are applied to an example concerning water resource bearing capacity. Recently, the Hesitant Fuzzy Linguistic Term Sets (HFLTSs) have been widely used to address cognitive complex linguistic information because of its advantage in representing vagueness and hesitation in qualitative decision-making process. Information measures, including distance measure, similarity measure, entropy measure, inclusion measure and correlation measure, are used to characterize the relationships between linguistic elements. Many decision-making theories are based on information measures. Up to now, distance, similarity, entropy and correlation measures have been proposed by scholars but there is no paper focuses on inclusion measure. This paper dedicates to filling this gap and the inclusion measure between HFLTSs are proposed. We discuss the relationships among distance, similarity, inclusion and entropy measures of HFLTSs. Given that clustering algorithm is an important application of information measures but there are few papers related to clustering algorithm based on information measures in the environment of HFLTS, in this paper, we propose two clustering algorithms based on correlation measure and distance measure, respectively. After that, a case study concerning water resource bearing capacity is illustrated to verify the applicability of the proposed clustering algorithms.