Fuzzy rough graphs via fuzzy graph ideals with applications

Dali Shi; Salah Eldin Abbas; Hossam M. Khiamy; Ismail Ibedou; Dali Shi; Salah Eldin Abbas; Hossam M. Khiamy; Ismail Ibedou

doi:10.3934/math.2026119

AIMS Mathematics

2026, Volume 11, Issue 1: 2979-3007. doi: 10.3934/math.2026119

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Fuzzy rough graphs via fuzzy graph ideals with applications

1.
College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China
2.
Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
3.
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

Received: 10 December 2025 Revised: 15 January 2026 Accepted: 19 January 2026 Published: 29 January 2026
MSC : 03E72, 68R05, 68R10

In this paper, we extend the concept of fuzzy rough sets to graphs by introducing the notion of "fuzzy graph ideals". This novel approach enables the construction of rough fuzzy digraphs, termed "fuzzy graph ideal approximation spaces", along with associated methods of formation. We define new fuzzy lower and upper graphs based on any two fuzzy binary relations on the vertex and edge sets of a directed graph thereby utilizing the concept of fuzzy graph ideals. Additionally, we explore fuzzy interior and fuzzy closure graphs within rough fuzzy graphs, and examine properties such as fuzzy graph connectedness through the application of these new operators. These developments offer valuable tools to address uncertain decision-making problems, with potential practical applications in various domains. Particularly, we provide an algorithm to solve decision-making problems regarding the identification of the best location in a department to set a mobile phone Jammer.
- fuzzy rough relations,
- fuzzy rough digraphs,
- fuzzy graph ideals,
- decision-making
Citation: Dali Shi, Salah Eldin Abbas, Hossam M. Khiamy, Ismail Ibedou. Fuzzy rough graphs via fuzzy graph ideals with applications[J]. AIMS Mathematics, 2026, 11(1): 2979-3007. doi: 10.3934/math.2026119

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Abstract

In this paper, we extend the concept of fuzzy rough sets to graphs by introducing the notion of "fuzzy graph ideals". This novel approach enables the construction of rough fuzzy digraphs, termed "fuzzy graph ideal approximation spaces", along with associated methods of formation. We define new fuzzy lower and upper graphs based on any two fuzzy binary relations on the vertex and edge sets of a directed graph thereby utilizing the concept of fuzzy graph ideals. Additionally, we explore fuzzy interior and fuzzy closure graphs within rough fuzzy graphs, and examine properties such as fuzzy graph connectedness through the application of these new operators. These developments offer valuable tools to address uncertain decision-making problems, with potential practical applications in various domains. Particularly, we provide an algorithm to solve decision-making problems regarding the identification of the best location in a department to set a mobile phone Jammer.

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