Abstract
This article first aims to critically review the existing literature on entropy measures for hesitant fuzzy elements (HFEs), and then introduces the concept of interval-transformed HFE (ITHFE) which bridges HFEs and interval-valued fuzzy sets (IVFSs). As discussed later, this bridge will also benefit researchers in terms of opening up more directions for future work, concentrating on HFE entropy measures. By taking the concept of ITHFE into account, we here exploit three features of an interval value including its lower and upper bounds, and the range of possible values to define a new class of entropy measures for HFEs. Then, we introduce the axiomatic framework of the new measures of entropy for HFEs, and two families of HFE entropy measures are also constructed. A comparison results shows that the proposed entropy measures for HFEs are more confident in distinguishing different HFEs rather than the most existing entropy measures. Finally, a multiple attribute decision making problem based on TOPSIS is applied to a case study of the health-care waste management.
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