Domination in Bipolar Fuzzy Rough Digraphs with Applications to Decision-Making

Authors

  • Anessa Arif Department of Mathematics, Faculty of Science, University of Faisalabad, Faisalabad, Pakistan
  • Aliya Fahmi Department of Mathematics, Faculty of Science, University of Faisalabad, Faisalabad, Pakistan
  • Aziz Khan Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
  • Aiman Mukheimer Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
  • Thabet Abdeljawad Department of Fundamental Sciences, Faculty of Engineering and Architecture, Istanbul Gelisim University, Avcılar-Istanbul, 34310, Turkiye
  • Rajermani Thinakaran Faculty of Data Science and Information Technology, INTI International University, Negeri Sembilan, Malaysia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6216

Keywords:

Bipolar Fuzzy Rough Set, Fuzzy Graphs, Domination number, Fuzzy Rough Digraphs, Regular Bipolar Fuzzy Graphs, Bipolar Fuzzy Graphs

Abstract

Fuzzy Rough Digraphs are insufficient for scenarios involving both positive and negative influences. To address the limitations of Fuzzy Rough Digraphs in modeling conflicting information, this paper introduces the Bipolar Fuzzy Rough Digraph (BFRD) as a new framework for decision-making under uncertainty. We define its fundamental properties, including the strength of paths, connectedness, vertex degree, the Regular BFRD. From these, we establish the concepts of the minimum dominating set and domination number. An algorithm is then developed to apply this framework to practical problems. The model’s efficacy is demonstrated through a real-world application: identifying an optimal set of rural areas for establishing medicine supply
markets by finding the minimum dominating set. This work provides a robust mathematical tool for solving complex problems involving bipolarity and as a process innovation.

Author Biography

  • Thabet Abdeljawad, Department of Fundamental Sciences, Faculty of Engineering and Architecture, Istanbul Gelisim University, Avcılar-Istanbul, 34310, Turkiye

    1-Department of Fundamental Sciences, Faculty of Engineering and Architecture, Istanbul Gelisim University, Avcılar-Istanbul, 34310, Turkiye

    2-Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833,
    11586 Riyadh, Saudi Arabia

    3- Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences
    University, Garankuwa, Medusa 0204, South Africa

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Mathematical and Fuzzy Logic

License

Copyright (c) 2025 A Arif, Aliya Fahmi, A Khan, T Abdeljawad, Rajermani Thinakaran

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How to Cite

Domination in Bipolar Fuzzy Rough Digraphs with Applications to Decision-Making. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6216. https://doi.org/10.29020/nybg.ejpam.v18i4.6216