Directional Shift-Stable Functions

Radko Mesiar and Andrea Stupňanová
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Radko Mesiar: Faculty of Civil Engineering, Slovakia University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
Andrea Stupňanová: Faculty of Civil Engineering, Slovakia University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia

Mathematics, 2021, vol. 9, issue 10, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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