A New Approach to Vague Soft Rough Topological Spaces

Authors

  • Raed Hatamleh Department of Mathematics, Faculty of Science, Jadara University, P.O. Box 733, Irbid 21110, Jordan
  • Haitham Alqawaqneh Al-Zaytoonah University of Jordan, Amman 11733, Jordan
  • Nasir Odat Department of mathematics, Faculty of Science, Jadara University, P.O. Box 733, Irbid 21110, Jordan;
  • Abdallah Al-Husban Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan;
  • Arif Mehmood Khattak Department of Mathematics and Statistics, Riphah International University, Sector I- 14, Islamabad, Pakistan
  • Alaa M. Abd El-latif Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Walid Abdelfattah Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • M. I. Elashiry Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Abdelhalim Hasnaoui Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6456

Keywords:

rough sets, vague soft rough sets, vague soft rough topology. vague soft rough open sets, vague soft rough close sets.

Abstract

In this particular piece of work, the new hybrid concept of vague soft rough set theory is introduced. It is a combination of rough set theory, soft set theory, and vague set theory. Based on this new concept, some definitions and operations are introduced. Furthermore, lower and upper vague soft approximations, vague soft rough positive, vague soft negative, and vague soft boundaries are discussed with examples. In addition, several theorems are presented in terms of lower and upper vague soft approximations, supported by examples for better understanding. Finally, an entirely new mathematical structure known as the vague soft rough topological structure is introduced. The related definitions of open sets, closed sets, closure, and interior, as well as their relationships in vague soft rough topological spaces, are addressed. To enhance understanding of this study, numerous examples are provided.

Author Biographies

  • Raed Hatamleh, Department of Mathematics, Faculty of Science, Jadara University, P.O. Box 733, Irbid 21110, Jordan

    Prof

  • Nasir Odat, Department of mathematics, Faculty of Science, Jadara University, P.O. Box 733, Irbid 21110, Jordan;

    Prof

  • Abdallah Al-Husban, Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan;

    Prof

  • Alaa M. Abd El-latif, Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

    Prof

  • Walid Abdelfattah, Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

    Prof

  • M. I. Elashiry, Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

    Prof

  • Abdelhalim Hasnaoui, Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

    Prof

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Topology

License

Copyright (c) 2025 Raed Hatamleh, Haitham Alqawaqneh, Nasir Odat, Abdallah Al-Husban, Arif Mehmood Khattak, Alaa M. Abd El-latif, Walid Abdelfattah, M. I. Elashiry, Abdelhalim Hasnaoui

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How to Cite

A New Approach to Vague Soft Rough Topological Spaces. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6456. https://doi.org/10.29020/nybg.ejpam.v18i3.6456