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

Authors

• Takaaki Fujita, Independent Researcher, Tokyo, JapanFollow
• Ajoy Kanti Das, Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, IndiaFollow
• Suman Das, Assistant Professor Grade II (Mathematics), Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, IndiaFollow
• Sankar Prasad Mondal, Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, 741249, West Bengal, IndiaFollow
• Volkan Duran, Department of Computer Engineering Igdır University, TurkeyFollow
• Mithun Datta, Department of Mathematics, ICFAI University Tripura, IndiaFollow

Authors' ORCIDs

Takaaki Fujita: https://orcid.org/0000-0002-9380-386X

Ajoy Kanti Das: https://orcid.org/0000-0002-9326-1677

Suman Das: https://orcid.org/0000-0001-5682-9334

Sankar Prasad Mondal: https://orcid.org/0000-0003-4690-2598

Volkan Duran: https://orcid.org/0000-0003-0692-0265

Mithun Datta: https://orcid.org/0009-0000-9172-7261

Article Type

Research Article

Abstract

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.

Keywords

Soft sets, Hypersoft sets, SuperHyperSoft sets, DiGraphicSoft sets, BiDiGraphicSoft sets

How to Cite

Fujita, Takaaki; Das, Ajoy Kanti; Das, Suman; Mondal, Sankar Prasad; Duran, Volkan; and Datta, Mithun (2026) "DiGraphicSoft Sets and BiDiGraphicSoft Sets: Directed and Bidirected Extensions of GraphicSoft Modeling," Neutrosophic Systems with Applications: Vol. 26: Iss. 7, Article 1. DOI: https://doi.org/10.63689/2993-7159.1353