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Top1. Introduction
In real-world decision-making, problems with uncertain conditions are common, but they are challenging due to the difficulty in coping with such uncertainty. Various probability models are helpful for such problems. However, in most situations, the uncertainty is imprecise or vague rather than probabilistic in nature. So, other models such as fuzzy set theory (Zadeh 1965) and fuzzy logic (Dubois and Prade 1980) have been successfully applied to handle imprecise or vague information. Some recent studies regarding fuzzy entropy and its generalizations are due to Singh and Sharma (2019), Joshi and Kumar (2017a, 2017b), and Tiwari (2021). These studies also deal with the applications in decision-making and pattern recognition. However, the modeling tools of ordinary fuzzy sets are limited when several sources of vagueness appear simultaneously. Due to this reason, various generalizations and extensions of fuzzy sets have been introduced, such as interval-valued fuzzy sets (IVFSs) (Zadeh 1975), intuitionistic fuzzy sets (IFSs) (Atanassov 1999), hesitant fuzzy sets (HFSs) (Torra 2010), etc. Some prominent studies regarding information measures in the intuitionistic fuzzy framework are due to Li and Chuntian (2002), Li (2004), Li and Ren (2015), Zhu and Li (2016), Ren et al. (2017), Wei et al. (2019) and Wei et al.(2021). In these studies, the proposed Intuitionistic fuzzy/Interval valued intuitionistic fuzzy information have been applied in the interdisciplinary applications. Recently, Augustine (2021) and Singh et al. (2021) presented some non-standard fuzzy correlation coefficients with their applications in pattern recognition problems. All of these extensions suit problems that are defined as quantitative situations. However, the information is usually unquantifiable in almost all real-life situations, i.e., qualitative, e.g., to evaluate a car's speed, we prefer terms like fast, average, slow, etc., rather than any numerical value. This is due to the unavailability of precise quantitative information or high computation cost. So, in order to deal with qualitative information, the fuzzy linguistic approach (Zadeh 1975) is applied, and it has given good results in different fields such as decision-making (Delgado et al. 1993), information retrieval (Bordonga and Passi 1993), marketing (Yager et al. 1994), education (Law 1996), etc. Nevertheless, the linguistic approaches have also got some severe limitations as these approaches use simple or single linguistic terms to access a linguistic variable that does not reflect the decision-maker's choice.
In most situations, experts hesitate among different linguistic terms to represent their opinions because of a lack of knowledge and information. Therefore, to represent their knowledge, only one linguistic term is not enough. Rodriguez et al. (2012) developed the notion of hesitant fuzzy linguistic terms set (HFLTS) from hesitant fuzzy sets (HFSs) (Torra 2010) and linguistic term sets (LTSs) (Zadeh 1975), in which the value of a linguistic variable is a continuous and ordered subset in a linguistic term set (LTS). For example, the LTS {”poor”, “good”, “very good”} expresses the degree of comfort of a car. The evaluation “at least good” can be represented in terms of an HFLTS as {”good”, “very good”} and can be considered as a generalized linguistic term “good” or “very good”. HFLTS is a powerful technique for an expert to express his/her opinion by using complex linguistic terms or single linguistic terms. Rodriguez et al. (2012) also examined various basic operations of HFLTSs and their properties. Liao et al. (2014) gave the mathematical representation of HFLTS and called the elements of HFLTS as hesitant fuzzy linguistic elements (HFLE). Liao et al. (2014) introduced various information measures like distance and similarity measures for HFLTS with their applications in MCDM. The theory of aggregation operators for HFLTS has been widely discussed by Wei et al. (2014). For further HFLTS applications, one can refer to (Liu et al. 2014; Liu and Rodriguez 2014; Rodriguez et al. 2014; Rodriguez et al. 2013; Zhu and Xu 2014).