DiGraphicSoft Sets and BiDiGraphicSoft Sets: Directed and Bidirected Extensions of GraphicSoft Modeling

Uncertainty has been modeled through a wide variety of mathematical frameworks, including fuzzy sets, neutrosophic sets, rough sets, and plithogenic sets. Among these approaches, soft sets offer a parameterized representation of uncertain information and have inspired numerous extensions, such as multisoft sets, double-framed soft sets, hypersoft sets, SuperHyperSoft sets, TreeSoft sets, ForestSoft sets, IndetermSoft sets, and IndetermHyperSoft sets.This paper focuses on GraphicSoft Sets, which extend the classical soft-set framework by assigning a subset of the universe to each subgraph of an attribute graph. In this way, relationships among attributes are incorporated directly into the parameterized model. Building on this structure, we introduce two directional generalizations, called DiGraphicSoft Sets and BiDiGraphicSoft Sets, based on directed graphs and bidirected graphs, respectively. Their basic properties are examined, and the role of directionality in enhancing the expressive capability of GraphicSoft modeling is discussed.