Introducing Soft Directed Hypergraphs: A Fusion of Soft Set Theory and Directed Hypergraphs

Directed hypergraphs represent a natural extension of directed graphs, while soft set theory provides a method for addressing vagueness and uncertainty. This paper introduces the notion of soft directed hypergraphs by integrating soft set principles into directed hypergraphs. Through parameterization, soft directed hypergraphs yield a sequence of relation descriptions derived from a directed hypergraph. Additionally, we present several operations for soft directed hypergraphs, including extended union, restricted union, extended intersection, and restricted intersection, and explore their characteristics.