Bipolar soft neighborhoods with application in decision-making

Authors

  • Saif Z. Hameed
    Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, 10001, Iraq
  • Heba I. Mustafa
    Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44511, Egypt
  • Abdelaziz E. Radwan
    Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, 11311, Egypt

Keywords:

Bipolar soft set, Binary bipolar soft set, Bipolar soft approximation, Bipolar soft neighborhoods

Abstract

This paper introduces bipolar soft (BS) neighborhood structures within the framework of soft set theory. First, several properties associated with lower and upper approximations based on a binary BS relation are examined, and the proposed approximation operators are shown to satisfy several fundamental properties. Next, an additional structure formulated through BS neighborhoods is explored. The concept of bipolar soft NjBS-neighborhood spaces is investigated, and their main characteristics are analyzed. Two types of topologies, overline{T}_zeta   and underline{T}_zeta, induced by bipolar soft reflexive relations are then characterized. These topological structures are used to approximate rough sets, and a direct method is proposed to generate such topologies from the underlying relations. Finally, a numerical example is provided to illustrate the applicability of the proposed approach to decision-making.

Dimensions

[1] D. Molodtsov, ``Soft set theory--first results'', Computers & Mathematics with Applications 37 (1999) 19. https://doi.org/10.1016/S0898-1221(99)00056-5.

[2] P. K. Maji, R. Biswas & A. R. Roy, ``Soft set theory'', Computers & Mathematics with Applications 45 (2003) 555. https://doi.org/10.1016/S0898-1221(03)00016-6.

[3] M. Shabir & M. Naz, ``On soft topological spaces'', Computers & Mathematics with Applications 61 (2011) 1786. https://doi.org/10.1016/j.camwa.2011.02.006.

[4] M. Akdag & A. Ozkan, ``Soft $alpha$-open sets and soft $alpha$-continuous functions'', Abstract and Applied Analysis 2014 (2014) 891341. https://doi.org/10.1155/2014/891341.

[5] M. Akdag & A. Ozkan, ``Soft $b$-open sets and soft $b$-continuous functions'', Mathematical Sciences 8 (2014) 124. https://doi.org/10.1007/s40096-014-0124-7.

[6] S. Z. Hameed, H. I. Mustafa, A. E. Radwan & E. El-Seidy, ``$N$-bipolar soft connectedness, disconnectedness and compactness spaces with application in infinite game'', Nonlinear Functional Analysis and Applications 30 (2025) 25. https://doi.org/10.22771/nfaa.2025.30.01.03.

[7] S. Z. Hameed, A. E. Radwan & E. El-Seidy, ``On soft strongly $b^*$-compactness and soft strongly $b^*$-connectedness in soft topological spaces'', Scalable Computing: Practice and Experience 25 (2024) 4335. https://doi.org/10.12694/scpe.v25i5.3178.

[8] S. Z. Hameed, A. E. Radwan & E. El-Seidy, ``On soft strongly $b^*$-separation axioms'', Iraqi Journal of Science 65 (2024) 3259. https://doi.org/10.24996/ijs.2024.65.6.25.

[9] A. E. Radwan, E. El-Seidy & S. Z. Hameed, ``On soft strongly $b^*$-closed via soft ideal'', Communications on Applied Nonlinear Analysis 31 (2024) 284. https://doi.org/10.52783/cana.v31.551.

[10] M. Shabir & M. Naz, ``On bipolar soft sets'', arXiv preprint arXiv:1303.1344 (2013). https://doi.org/10.48550/arXiv.1303.1344.

[11] F. Fatimah, D. Rosadi, R. B. F. Hakim & J. C. R. Alcantud, ``$N$-soft sets and their decision-making algorithms'', Soft Computing 22 (2018) 3829. https://doi.org/10.1007/s00500-017-2838-6.

[12] A. Fadel & S. C. Dzul-Kifli, ``Bipolar soft topological spaces'', European Journal of Pure and Applied Mathematics 13 (2020) 227. https://doi.org/10.29020/nybg.ejpam.v13i2.3645.

[13] O. Dalkılıç & N. Demirtaş, ``Binary bipolar soft sets'', Boletim da Sociedade Paranaense de Matem'atica 41 (2023) 1. https://doi.org/10.5269/bspm.51003.

[14] Z. Pawlak, ``Rough sets'', International Journal of Computer and Information Sciences 11 (1982) 341. https://doi.org/10.1007/BF01001956.

[15] M. E. Abd El-Monsef, O. A. Embaby & M. K. El-Bably, ``Comparison between rough set approximations based on different topologies'', International Journal of Granular Computing, Rough Sets and Intelligent Systems 3 (2015) 292. https://doi.org/10.1504/IJGCRSIS.2014.068032.

[16] R. Abu-Gdairi, M. A. El-Gayar, T. M. Al-shami, A. S. Nawar & M. K. El-Bably, ``Some topological approaches for generalized rough sets and their decision-making applications'', Symmetry 14 (2022) 95. https://doi.org/10.3390/sym14010095.

[17] M. Shabir, R. S. Kanwal & M. I. Ali, ``Reduction of an information system'', Soft Computing 24 (2020) 10801. https://doi.org/10.1007/s00500-019-04582-3.

[18] D. Dubois & H. Prade, ``An introduction to bipolar representations of information and preference'', International Journal of Intelligent Systems 23 (2008) 866. https://doi.org/10.1002/int.20297.

[19] A. M. Ramadhan, ``Bipolar soft minimal structures'', European Journal of Pure and Applied Mathematics 18 (2025) 5928. https://doi.org/10.29020/nybg.ejpam.v18i2.5928.

[20] I. T. Shbair, A. S. Salama, O. A. Embaby & A. A. El-Atik, ``Some topological approaches of rough sets through minimal neighborhoods and decision making'', Journal of Mathematics 2024 (2024) 2214422. https://doi.org/10.1155/2024/2214422.

[21] S. S. Mohammed, ``On fuzzy soft set-valued maps with application'', Journal of the Nigerian Society of Physical Sciences 2 (2020) 26. https://doi.org/10.46481/jnsps.2020.48.

[22] P. A. Ejegwa, I. C. Onyeke, B. T. Terhemen, M. P. Onoja, A. Ogiji & C. U. Opeh, ``Modified Szmidt and Kacprzyk's intuitionistic fuzzy distances and their applications in decision-making'', Journal of the Nigerian Society of Physical Sciences 4 (2022) 174. https://doi.org/10.46481/jnsps.2022.530.

[23] B. P. Varol & H. Malkoc{c}, ``Bipolar fuzzy supra topology via (Q-) neighborhood and its application in data mining process'', Symmetry 16 (2024) 216. https://doi.org/10.3390/sym16020216.

[24] R. A. Hosny, R. Abu-Gdairi & M. K. El-Bably, ``Enhancing dengue fever diagnosis with generalized rough sets: utilizing initial-neighborhoods and ideals'', Alexandria Engineering Journal 94 (2024) 68. https://doi.org/10.1016/j.aej.2024.03.028.

[25] H. I. Mustafa & R. Wassef, ``Improved soft rough approximations based on soft neighborhoods'', Filomat 39 (2025) 4887. https://doi.org/10.2298/FIL2514887M.

Q1

Published

2026-08-04

How to Cite

Bipolar soft neighborhoods with application in decision-making. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3337. https://doi.org/10.46481/jnsps.2026.3337

Issue

Volume 8, Issue 3, August 2026 (In Progress)

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Saif Z. Hameed, Heba I. Mustafa, Abdelaziz E. Radwan (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Bipolar soft neighborhoods with application in decision-making. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3337. https://doi.org/10.46481/jnsps.2026.3337

Similar Articles

51-60 of 63

You may also start an advanced similarity search for this article.