Summary: Based on a new hesitant fuzzy partial ordering proposed by L. Garmendia et al. [Int. J. Approx. Reasoning 84, 159–167 (2017; Zbl 1422.03116)], in this paper, a fuzzy disjunction \(D\) on the set \(H\) of finite and nonempty subsets of the unit interval and a t-conorm \(S\) on the set \(\bar{B}\) of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations \(N_n\) on \(H\) and \(mu_n\) on \(\bar{B}\) are proposed. Particularly, their De Morgan’s laws are investigated with respect to binary operations \(C\) and \(D\) on \(H\), as well as \(T\) and \(S\) on \(\bar{B}\), respectively, where \(C\) is a commutative fuzzy conjunction on \((H,\leq_H)\) and \(T\) is a t-norm on \((\bar{B},\leq_B)\). Finally, the new hesitant fuzzy aggregation operators are presented on \(H\) and \(\bar{B}\) and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making.