On (r)over-right-arrow-(Quasi-)Overlap Functions

Overlap functions, as one kind of particular binary aggregation functions, have been continuously studied in the literature for their vast preponderance in some real applications. Meanwhile, after Lucca et al. introduced the notion of preaggregation functions recently, the investigation related to such aggregation functions becomes an interesting, and natural research area. In this article, we continue to focus on this topic for overlap functions. First, we introduce the concept of (r) over right arrow-(quasi-)overlap functions by replacing the monotonicity of (quasi-)overlap functions with directional monotonicity, and the notions of 0-(r) over right arrow-(quasi-)overlap functions, 1-(r) over right arrow-(quasi-)overlap function, and 0,1-(r) over right arrow-(quasi-)overlap functions associated with them. And then, we propose some vital properties of (r) over right arrow-(quasi-)overlap functions. Finally, we show several construction methods of (r) over right arrow-(quasi-)overlap functions, 0-(r) over right arrow-(quasi)overlap functions, 1-(r) over right arrow-(quasi-)overlap function, and 0,1-(r) over right arrow-(quasi)overlap functions.

Automated summary

The article focuses on overlap functions, introducing the concept of (r) over right arrow-(quasi-)overlap functions and their associated properties. Several construction methods for these functions are also proposed, contributing to the research in this area.