Directional Shift-Stable Functions

Abstract

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.

Keywords

• aggregation function
• directional monotonicity
• pre-aggregation function
• shift invariantness