Recently, some new types of monotonicity—in particular, weak monotonicity and directional monotonicity of an n-ary real function—were introduced and successfully applied. Inspired by these generalizations of monotonicity, we introduce a new notion for n-ary functions acting on ${[0,1]}^n$, namely, the directional shift stability. This new property extends the standard shift invariantness (difference scale invariantness), which can be seen as a particular directional shift stability. The newly proposed property can also be seen as a particular kind of local linearity. Several examples and a complete characterization for the case of $n=2$ of directionally shift-stable aggregation and pre-aggregation functions are also given.

中文翻译：

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方向移位稳定功能

最近，引入并成功地应用了一些新的类型的单调性，特别是n元实函数的弱单调性和方向单调性。受这些单调性概括的启发，我们为作用于n元函数的n元函数引入了一个新概念${[0，\mathrm{1个}]}^{ñ}$，即方向偏移稳定性。此新属性扩展了标准位移不变性（差异标度不变性），可以将其视为特定的方向位移稳定性。新提议的属性也可以视为一种特殊的局部线性。几个例子和一个完整的表征情况$ñ=\mathrm{2个}$ 还给出了方向移位稳定的聚集和预聚集函数的示意图。