Soft convex structures

TL;DR

This paper introduces the concept of soft convex structures, exploring their properties and defining related soft convex sets, hulls, and operators to extend classical convex analysis into a soft set framework.

Contribution

It presents the first systematic study of soft convex structures, defining key concepts and examining their properties and relationships to classical convex structures.

Findings

Defined soft convex sets, concave sets, and hull operators.

Investigated properties of soft convex structures.

Explored relationships between soft convex bases and convex structures.

Abstract

In this manuscript the idea of soft convex structures is given and some of their properties are investigated. Also, soft convex sets, soft concave sets and soft convex hull operator are defined and their properties are studied. Moreover, the concepts of soft convexly derived operator and soft convex base are studied and their relationship to convex structures are explored.