Convex Soft Geometries

Abstract

This paper introduces convex soft geometries. The import of this model is that it extends a successful field of research, namely, convex geometries, to account for alternatives characterized by a multiplicity of attributes. Related concepts include soft convex hulls and a notion of extreme elements. Some fundamental results are proven. Among them, we guarantee that an anti-exchange property holds true. Importantly, the existence of extreme elements is guaranteed hence proving their suitability for applied studies. Both results are natural (but non-trivial) extensions of comparable outputs for convex geometries. We present a detailed research program that might stimulate future investigations on this new research area.

Received: 17 December 2021 | Revised: 29 December 2021 | Accepted: 19 January 2022

Conflicts of Interest

José Carlos R. Alcantud is an editorial board member for Journal of Computational and Cognitive Engineering, and was not involved in the editorial review or the decision to publish this article. The author declares that he has no conflicts of interest to this work.