Bent functions $f: V_{n}\rightarrow \mathbb{F}_{p}$ with certain additional properties play an important role in constructing partial difference sets, where $V_{n}$ denotes an $n$-dimensional vector space over $\mathbb{F}_{p}$, $p$ is an odd prime. In \cite{Cesmelioglu1,Cesmelioglu2}, the so-called vectorial dual-bent functions are considered to construct partial difference sets. In \cite{Cesmelioglu1}, \c{C}e\c{s}melio\v{g}lu \emph{et al.} showed that for vectorial dual-bent functions $F: V_{n}\rightarrow V_{s}$ with certain additional properties, the preimage set of $0$ for $F$ forms a partial difference set. In \cite{Cesmelioglu2}, \c{C}e\c{s}melio\v{g}lu \emph{et al.} showed that for a class of Maiorana-McFarland vectorial dual-bent functions $F: V_{n}\rightarrow \mathbb{F}_{p^s}$, the preimage set of the squares (non-squares) in $\mathbb{F}_{p^s}^{*}$ for $F$ forms a partial difference set. In this paper, we further study vectorial dual-bent functions and partial difference sets. We prove that for vectorial dual-bent functions $F: V_{n}\rightarrow \mathbb{F}_{p^s}$ with certain additional properties, the preimage set of the squares (non-squares) in $\mathbb{F}_{p^s}^{*}$ for $F$ and the preimage set of any coset of some subgroup of $\mathbb{F}_{p^s}^{*}$ for $F$ form partial difference sets. Furthermore, explicit constructions of partial difference sets are yielded from some (non)-quadratic vectorial dual-bent functions. In this paper, we illustrate that almost all the results of using weakly regular $p$-ary bent functions to construct partial difference sets are special cases of our results.

翻译：Bent 函数 $f: V ⁇ n{rrightror\ mathb{F}}} 具有某些附加属性的所谓矢量双倍函数在构建部分差异设置中扮演了重要角色。 在\\ {cn{crright{F}} 在构建部分差异设置中, $V{n} 美元表示在$\mab{F} 美元上, 美元是一个奇数。 在\ cite{cite{Ceseliob{ f} 美元中, 所谓的矢量双倍函数被视为构建部分差异设置。 在\ cite{cite{cite{celio} com_ 美元1},\c{c{cr\c} meliet\ v} g{g} liet{g} spreme} 表示,对于矢量的双倍矢量功能 $F: V{rightrrror%s) 预设定美元构成部分差异。 在\\\\ max max max max max max a remade max a remax a remax max max romax rode ro ro ro ro rode ro ro ro ro ro ro rode rode ro ro ro ro ro ro ro ro ro ro ro ro rops a s ms ms ms romas a a a s s s s ms s s s s mets a a a a a a a a s