Directional Shift-Stable Functions

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.

Automated summary

Novel concepts of directional shift stability for n-ary functions acting on [0,1](n) are introduced in this paper, extending the standard shift invariantness and can also be viewed as a specific type of local linearity. The article also provides several examples and a comprehensive characterization of directionally shift-stable aggregation and pre-aggregation functions for the case of n=2.