Total orders of extended hesitant fuzzy linguistic term sets: Definitions, generations and applications

Abstract

Extended hesitant fuzzy linguistic term sets (EHFLTSs) are helpful to model uncertain linguistic information in qualitative group decision making (QGDM). Total orders are essentialwhenever more than two EHFLTSs have to be compared, such as aggregating them by the ordered weighted averaging (OWA) operator. However, the existing studies only focus on partial orders of EHFLTSs and thus their application may be limited. The main purpose of this paper is to develop total orders of EHFLTSs. A constructive approach is proposed to generate total orders by aggregation functions. Three distinct total orders are defined for potential applications as well. To clarify the importance of total orders in QGDM, the extended hesitant fuzzy linguistic OWA operator is developed and some properties are demonstrated. Finally, based on the proposed techniques and the social choice theory, an approach formed by two algorithms is presented to solve the QGDM problems in which some necessary parameters, e.g. risk preferences, are complicated to determine. The proposed total order resolves one current challenge of EHFLTSs and thus can serve as a foundation of decision making with EHFLTSs.