Negations and aggregation operators based on a new hesitant fuzzy partial ordering

Abstract

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, 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.