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Hesitant fuzzy linguistic term set (HFLTS) is very useful in depicting the situations where people are hesitant to provide their opinions or assessments. In a HFLTS, it should be considered two types of uncertainty, fuzziness and hesitation. This paper is aimed to investigate the problem of how apply different uncertainty facets in different decision making settings. First, a new construction method of a fuzzy entropy for HFLTSs is proposed and it is compared with other methods already introduced in the literatures. Afterwards, these entropy formulas are used to propose two algorithms for deriving the criteria weights and experts weights. Different from the existing applications, it is stressed that in the process of deriving the criteria weights, only the hesitancy of the HFLTS should be considered, while in the process of deriving the experts weights with hesitant fuzzy preference relation information, both the fuzziness and …