Uncertainty Measures of Extended Hesitant Fuzzy Linguistic Term Sets

A hesitant fuzzy linguistic term set (HFLTS) is defined as a subset of ordered consecutive linguistic terms, and it has been successfully applied to deal with experts hesitation in decision-making problems when experts have to provide their assessments. This concept has been recently extended to manage ordered consecutive and nonconsecutive linguistic terms, called extended HFLTS (EHFLTS), which is used in linguistic group decision-making problems to represent the group opinion without loss of information. This paper is focused on studying how to measure the uncertainty presented by the information of an EHFLTS and also of an HFLTS. To do so, a new comprehensive entropy measure for EHFLTSs, which considers two types of uncertainty, fuzziness and hesitation, is proposed. The construction methods of the two types of entropy are studied and a comprehensive entropy formula is defined. Finally, a comparative study is carried out to analyze the results obtained from the proposed entropy measures.