The notion of betweenness space or of a convex structure is an abstraction of the standard notion of convexity in a linear space. We first consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness. We study morphism between abstract convex spaces and we characterize aggregation function that are monotone with respect to a betweenness relation.
Betweenness Spaces: Morphism and Aggregation Functions
Cardin, Marta
2019
Abstract
The notion of betweenness space or of a convex structure is an abstraction of the standard notion of convexity in a linear space. We first consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness. We study morphism between abstract convex spaces and we characterize aggregation function that are monotone with respect to a betweenness relation.
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