AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Fuzzy Information and Engineering Article
PDF (4.7 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Article | Open Access

Novel Classes of Bipolar Soft Generalized Topological Structures: Compactness and Homeomorphisms

Hind Y. Saleh1, Baravan A. Asaad2,3 ( ), Ramadhan A. Mohammed1
Department of Mathematics, College of Basic Education, University of Duhok, Duhok 42001, Iraq
Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq
Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Iraq
Show Author Information

Abstract

The purpose of this paper is to define bipolar soft generalized compact sets and bipolar soft generalized compact spaces. The structures of g~~-centralized bipolar soft generalized closed sets collection in a bipolar soft generalized compact space are given. Moreover, some main properties of bipolar soft generalized compactness are discussed and their relationships are studied. The concept of a bipolar soft generalized compactness is introduced and it investigates under what condition a bipolar soft generalized topological space forms a bipolar soft generalized compact space. The relation between bipolar soft generalized compact space and soft generalized compact space is proposed. Furthermore, some further properties of bipolar soft mappings, such as bipolar soft composite mappings, are presented and some of their characteristics are explained. Additionally, novel classes of bipolar soft mapping such as bipolar soft generalized continuous, bipolar soft generalized open, and bipolar soft generalized closed mappings are defined. Finally, some results and counterexamples are obtained.

Keywords

bipolar soft generalized compact space (set)bipolar soft generalized continuous mappingsbipolar soft generalized homeomorphism mappings

References

[1]

D. Molodtsov, Soft set theory—First results, Comput. Math. Appl., vol. 37, nos. 4&5, pp. 19–31, 1999.
Crossref Google Scholar
[2]

P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Comput. Math. Appl., vol. 45, nos. 4&5, pp. 555–562, 2003.
Crossref Google Scholar
[3]

N. Çağman and S. Enginoğlu, Soft set theory and uni–int decision making, Eur. J. Oper. Res., vol. 207, no. 2, pp. 848–855, 2010.
Crossref Google Scholar
[4]

H. Aktaş and N. Çağman, Soft sets and soft groups, Inf. Sci. Int. J., vol. 177, no. 13, pp. 2726–2735, 2007.
Crossref Google Scholar
[5]

M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., vol. 61, no. 7, pp. 1786–1799, 2011.
Crossref Google Scholar
[6]

N. Çağman, S. Karataş, and S. Enginoglu, Soft topology, Comput. Math. Appl., vol. 62, no. 1, pp. 351–358, 2011.
Crossref Google Scholar
[7]

Z. M. Ma, W. Yang, and B. Q. Hu, Soft set theory based on its extension, Fuzzy Information and Engineering, vol. 2, no. 4, pp. 423–432, 2010.
Crossref Google Scholar
[8]

Z. A. Ameen and S. Al Ghour, Minimal soft topologies, New Math. And Nat. Computation, vol. 19, no. 1, pp. 19–31, 2023.
Crossref Google Scholar
[9]

Z. A. Ameen and M. H. Alqahtani, Some classes of soft functions defined by soft open sets modulo soft sets of the first category, Mathematics, vol. 11, no. 20, p. 4368, 2023.
Crossref Google Scholar
[10]

Z. A. Ameen and M. H. Alqahtani, Congruence representations via soft ideals in soft topological spaces, Axioms, vol. 12, no. 11, p. 1015, 2023.
Crossref Google Scholar
[11]

Á. Császár, Generalized topology, generized continuity, Acta Math. Hung., vol. 96, no. 4, pp. 351–357, 2002.
Crossref Google Scholar
[12]

Á. Császár, Mixed constructions for generalized topologies, Acta Math. Hung., vol. 122, no. 1, pp. 153–159, 2009.
Crossref Google Scholar
[13]
M. Shabir and M. Naz, On bipolar soft sets, arXiv preprint arXiv: 1303.1344, 2013.
[14]

M. Naz and M. Shabir, On fuzzy bipolar soft sets, their algebraic structures and applications, J. Intell. Fuzzy Syst., vol. 26, no. 4, pp. 1645–1656, 2014.
Crossref Google Scholar
[15]

D. Dubois and H. Prade, An introduction to bipolar representations of information and preference, Int. J. Intell. Syst., vol. 23, no. 8, pp. 866–877, 2008.
Crossref Google Scholar
[16]

A. Fadel and S. C. Dzul-Kifli, Bipolar soft topological spaces, Eur. J. Pure Appl. Math., vol. 13, no. 2, pp. 227–245, 2020.
Crossref Google Scholar
[17]

A. Fadel and S. C. Dzul-Kifli, Bipolar soft functions, AIMS Math., vol. 6, no. 5, pp. 4428–4446, 2021.
Crossref Google Scholar
[18]

T. Y. Öztürk, On bipolar soft topological spaces, J. New Theo., vol. 20, pp. 64–75, 2018.
Google Scholar
[19]

T. Y. Öztürk, On bipolar soft points, TWMS J. App. Eng. Math., vol. 10, no. 4, pp. 877–885, 2020.
Google Scholar
[20]

T. S. Dizman and T. Y. Öztürk, Fuzzy bipolar soft topological spaces, TWMS J. App. Eng. Math., vol. 11, no. 1, pp. 151–159, 2021.
Google Scholar
[21]

S. Abdullah, M. Aslam, and K. Ullah, Bipolar fuzzy soft sets and its applications in decision making problem, J. Intell. Fuzzy Syst., vol. 27, no. 2, pp. 729–742, 2014.
Crossref Google Scholar
[22]

T. M. Al-shami, Bipolar soft sets: Relations between them and ordinary points and their applications, Complexity, vol. 2021, p. 6621854, 2021.
Crossref Google Scholar
[23]

F. Karaaslan and S. Karataş, A new approach to bipolar soft sets and its applications, Discrete Math. Algorithm. Appl., vol. 7, no. 4, p. 1550054, 2015.
Crossref Google Scholar
[24]

F. Karaaslan, A. Ullah, and I. Ahmad, Normal bipolar soft subgroups, Fuzzy Information and Engineering, vol. 13, no. 1, pp. 79–98, 2021.
Crossref Google Scholar
[25]

T. Mahmood, A novel approach towards bipolar soft sets and their applications, J. Math., vol. 2020, p. 4690808, 2020.
Crossref Google Scholar
[26]

J. Y. Wang, Y. P. Wang, and L. Liu, Hesitant bipolar-valued fuzzy soft sets and their application in decision making, Complexity, vol. 2020, p. 6496030, 2020.
Crossref Google Scholar
[27]

U. U. Rehman and T. Mahmood, Picture fuzzy N-soft sets and their applications in decision-making problems, Fuzzy Information and Engineering, vol. 13, no. 3, pp. 335–367, 2021.
Crossref Google Scholar
[28]

S. Hussain, Binary soft connected spaces and an application of binary soft sets in decision making problem, Fuzzy Information and Engineering, vol. 11, no. 4, pp. 506–521, 2019.
Crossref Google Scholar
[29]

S. Bera and M. Pal, On m-polar interval-valued fuzzy graph and its application, Fuzzy Information and Engineering, vol. 12, no. 1, pp. 71–96, 2020.
Crossref Google Scholar
[30]

M. Shabir and A. Bakhtawar, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songk. J. Sci. Technol., vol. 39, no. 3, pp. 359–371, 2017.
Google Scholar
[31]
C. G. Aras and S. Bayramov, Compactness on bipolar soft topological spaces, https://doi.org/10.22541/au.164864846.65181737/v1, 2022.
Crossref
[32]

S. Y. Musa and B. A. Asaad, Bipolar hypersoft sets, Mathematics, vol. 9, no. 15, p. 1826, 2021.
Crossref Google Scholar
[33]

S. Y. Musa and B. A. Asaad, Topological structures via bipolar hypersoft sets, J. Math., vol. 2022, p. 2896053, 2022.
Crossref Google Scholar
[34]

S. Y. Musa and B. A. Asaad, Bipolar hypersoft homeomorphism maps and bipolar hypersoft compact spaces, Int. J. Neutrosophic Sci., vol. 19, no. 2, pp. 95–107, 2022.
Crossref Google Scholar
[35]

H. Y. Saleh, B. A. Asaad, and R. A. Mohammed, Bipolar soft generalized topological structures and their application in decision making, Eur. J. Pure Appl. Math., vol. 15, no. 2, pp. 646–671, 2022.
Crossref Google Scholar
[36]

H. Y. Saleh, B. A. Asaad, and R. A. Mohammed, Bipolar soft limit points in bipolar soft generalized topological spaces, Math. Stat., vol. 10, no. 6, pp. 1264–1274, 2022.
Crossref Google Scholar
[37]

H. Y. Saleh, B. A. Asaad, and R. A. Mohammed, Connectedness, local connectedness, and components on bipolar soft generalized topological spaces, J. Math. Computer Sci., vol. 30, no. 4, pp. 302–321, 2023.
Crossref Google Scholar
[38]

Aras C. G., Al-shami T. M., and A. Mhemdi, S. Bayramov, Local compactness and paracompactness on bipolar soft topological spaces, J. Intell. Fuzzy Syst., vol. 43, no. 5, pp. 6755–6763, 2022.
Crossref Google Scholar
Fuzzy Information and Engineering
Volume 16 Issue 1,
March 2024
Pages 49-73
DOI: 10.26599/FIE.2023.9270031
Cite this article:
Saleh HY, Asaad BA, Mohammed RA. Novel Classes of Bipolar Soft Generalized Topological Structures: Compactness and Homeomorphisms. Fuzzy Information and Engineering, 2024, 16(1): 49-73. https://doi.org/10.26599/FIE.2023.9270031

377

Views

43

Downloads

0

Crossref

0

Web of Science

0

Scopus

Altmetrics
Received: 10 October 2023
Revised: 21 November 2023
Accepted: 31 December 2023
Published: 30 March 2024
© The Author(s) 2024. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Return