Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making

Hesitant fuzzy sets, originally proposed by Torra, can be used as an efficient tool for dealing with situations in which experts hesitate between several numerical values to define the membership of an element in a quantitative setting. However, similar situations may occur in qualitative settings where experts hesitate between several possible linguistic terms to assess the membership of an element. To deal with such cases, Rodriguez et al. [21] introduced the concept of a hesitant fuzzy linguistic term set (HFLTS). A hesitant fuzzy linguistic term set is an ordered finite subset of consecutive linguistic terms of a linguistic term set. However, it is noted that there are situations where the linguistic terms contained in the hesitant fuzzy linguistic term set are not consecutive. To address this issue, in this paper, we extend the hesitant fuzzy linguistic term set and introduce the concept of a hesitant fuzzy linguistic set (HFLS) by combining the hesitant fuzzy set and the fuzzy linguistic approach. Then, we develop some hesitant fuzzy linguistic aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy linguistic sets (HFLSs). We also investigate the relationships among these operators. Furthermore, we extend the hesitant fuzzy linguistic set to uncertain linguistic environments, i.e., present the concept of a hesitant fuzzy uncertain linguistic set (HFULS). We develop some hesitant fuzzy uncertain linguistic aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy uncertain linguistic sets (HFULSs). We study the relationships among these operators. Next, we utilize the hesitant fuzzy linguistic aggregation operators to develop an approach to multiple attribute group decision making with hesitant fuzzy linguistic information and utilize the hesitant fuzzy uncertain linguistic aggregation operators to develop an approach to multiple attribute group decision making with hesitant fuzzy uncertain linguistic information. Finally, we apply both the developed approaches to two numerical examples.