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Purpose -The purpose of this paper is to present some dynamic hesitant fuzzy aggregation operators to tackle with the multi-period decision-making problems where all decision information is provided by decision makers in hesitant fuzzy information from different periods. Design/methodology/approach -First, the notions and operational laws of the hesitant fuzzy variable are defined. Then, some dynamic hesitant fuzzy aggregation operators involve the dynamic hesitant fuzzy weighted averaging (DHFWA) operator, the dynamic hesitant fuzzy weighted geometric (DHFWG) operator, and their generalized versions are presented. Some desirable properties of these proposed operators are established. Furthermore, two linguistic quantifier-based methods are introduced to determine the weights of periods. Next, the paper extends the results to the interval-valued hesitant fuzzy situation. Furthermore, the authors develop an approach to solve the multi-period multiple criteria decision making (MPMCDM) problems. Finally, an illustrative example is given. Findings -The presented hesitant fuzzy aggregation operators are very suitable for aggregating the hesitant fuzzy information collected at different periods. The developed approach can solve the MPMCDM problems where all decision information takes the form of hesitant fuzzy information collected at different periods. Practical implications -The presented hesitant fuzzy aggregation operators and decision-making approach can widely apply to dynamic decision analysis, multi-stage decision analysis in real life. Originality/value -The paper presents the useful way to aggregate the hesitant fuzzy information collected at different periods in MPMCDM situations.