Q-Complex Neutrosophic Set

Ashraf; Abd Ghafur; Faisal; Abdalwali

doi:https://doi.org/10.54216/IJNS.200201

Full Length Article

Volume 20 • Issue 2 • PP: 08-19 • 2023

Q-Complex Neutrosophic Set

Ashraf Al-Quran ^1*

mail

,

Abd Ghafur Ahmad ²

mail

,

Faisal Al-Sharqi ³

mail

,

Abdalwali Lutfi ⁴

mail

¹Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia

²Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Malaysia

³Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq

⁴Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.200201

format_quote Cite this article

Received: July 26, 2022 Accepted: January 16, 2023

View PDF open_in_new

Abstract

Most complex problems in the real-world typically involve uncertain,incomplete and indeterminate two-dimensional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet the demand for models that has the ability to handle these information with these characteristics, the introduction of neutrosophic sets (NSs) was followed by their extension to the complex neutrosophic sets (CNSs). In this paper, we introduce the concept of Q- complex neutrosophic set (Q-CNS) by extending the ranges of the membership functions in Q-neutrosophic set (Q-NS) from [0,1] to the unit circle in the complex plane. Q-CNS plays a key role in the decision making theory, where the extra information provided by the elements of the Q-set serve in modeling of some decision making problems. Based on this new concept we define the basic theoretical operations such as complement, equality, subset, union, intersection, Q-complex neutrosophic product and Cartesian product. Some related examples are also given to enhance the understanding of the proposed concepts. The basic properties of these operators are also verified with supporting proofs.

Keywords

Complex Neutrosophic Set Decision Making Neutrosophic Set Q-Neutrosophic Set.

References

[1] Y. B. Jun, Q-Fuzzy subalgebras of BCK/BCI-algebras, Scientiae Mathematicae Japonicae Online, vol. 4, pp. 197–202, 2001.

[2] E. H. Roh, K. H. Kim, J. G. Lee, Intuitionistic Q-fuzzy subalgebras of BCK/BCI-algebras, International Mathematical Forum,vol. 1, pp. 1167–1174, 2006.

[3] O.Kazancı, S. Yamak, S. Yilmaz, On intuitionistic Q-fuzzy R-subgroups of near-rings, International Mathematical Forum, vol. 2, pp. 2899–2910, 2007.

[4] A. Solairaju, R. Nagarajan, A new structure and construction of Q-fuzzy groups, Advances in Fuzzy Mathematics, vol. 4 , pp. 23-29, 2009.

[5] R. Muthuraj, P. M. Sithar Selvam, M. S. Muthuraman, Anti Q-fuzzy group and its lower level subgroups, International Journal of Computer Applications, vol. 3, pp. 16-20, 2010.

[6] V. Lakshmana Gomathi Nayagam, R. Muthuraj, K. H. Manikandan, Intuitionistic Q-fuzzy HX group, International Journal of Mathematical Archive, vol. 2 , pp. 1133-1139, 2011.

[7] P. M. Sithar Selvam, T. Priya, T. Ramachandran, K. T. Nagalakshmi, Anti Q-fuzzy R-closed KU-ideals in KU-algebras and its lower level cuts, International Journal of Fuzzy Mathematical Archive, vol. 4 , pp. 61-71, 2014.

[8] K. Tanamoon, S. Sripaeng, A. Iampan, Q-Fuzzy sets in UP-algebras, Songklanakarin Journal of Science and Technology, vol. 40 , pp. 9-29, 2018.

[9] M. Abu Qamar, N. Hassan, An approach toward a Q-neutrosophic soft set and its application in decision making, Symmetry, vol. 11 , pp. 139, 2019.

[10] S. Thiruveni, A. Solairaju, Neutrosophic Q-fuzzy subgroups, International Journal of Mathematics And its Applications, vol. 6 , pp. 859-866, 2018.

[11] F. Adam, N. Hassan, Q-fuzzy soft set, Applied Mathematical Sciences, vol. 8 , pp. 8689-8695, 2014.

[12] S. Broumi, Q-Intuitionistic fuzzy soft sets, Journal of New Theory, vol. 5 , pp. 80-91, 2015.

[13] T. Mahmood, Q. Khan, M. A. Khan, Q-Single valued neutrosophic soft sets, Journal of New Theory, vol. 13 , pp. 10-25, 2016.

[14] M. Abu Qamar, N. Hassan, Q-Neutrosophic soft relation and its application in decision making, Entropy, vol. 20 , pp. 170, 2018.

[15] F. Smarandache, Neutrosophic probability, set, and logic, American Research Press: Rehoboth, IL, USA, 1998.

[16] F. Smarandache, Neutrosophic set- a generalisation of the intuitionistic fuzzy sets, International Journal

of Pure and Applied Mathematics, vol. 24 , pp. 287-297, 2005.

[17] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Multispace Multistructure, vol.4 , pp. 410-413, 2010.

[18] M. Ali, F. Smarandache, Complex neutrosophic set, Neural Computing and Applications, vol.28 , pp. 1817-1834, 2017.

[19] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy Systems, vol.10 , pp. 171-186, 2002.

[20] A. Alkouri, A. R. Salleh, Complex intuitionistic fuzzy sets, AIP Conference Proceedings, 1482, 464-470, 2012.

[21] A. Al-Quran, S. Alkhazaleh, Relations between the complex neutrosophic sets with their applications in decision making, Axioms, vol.7 , pp. 64, 2018.

[22] M. Ali, L.Q. Dat, L. H. Son, F. Smarandache, Interval complex neutrosophic set: formulation and applications in decision-making, International Journal of Fuzzy Systems, vol.20 , pp. 986-999, 2018.

[23] A. Al-Quran, N.Hassan, The complex neutrosophic soft expert set and its application in decision making, Journal of Intelligent and Fuzzy Systems, vol.34 , pp. 569-582, 2018.

[24] F. Al-Sharqi, A. Al-Quran, A.G. Ahmad, S. Broumi, Interval-valued complex neutrosophic soft set and its applications in decision-making, Neutrosophic Sets and Systems, vol.40 , pp. 149-168, 2021.

[25] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Interval-valued neutrosophic soft expert set from real space to complex space, Computer Modeling in Engineering and Sciences, vol.132 , pp. 267-293, 2022.

[26] A. Al-Quran, S. Alkhazaleh, L. Abdullah, Complex bipolar- valued neutrosophic soft set and its decision making method, Neutrosophic Sets and Systems, vol.47 , pp. 105-116, 2021.

[27] A. Al-Quran, N.Hassan, The complex neutrosophic soft expert relation and its multiple attribute decisionmaking method, Entropy,vol.20 , pp. 101, 2018.

[28] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Interval complex neutrosophic soft relations and their application in decision-making, Journal of Intelligent and Fuzzy Systems, vol.43 , pp. 745-771, 2022.

Cite This Article

Choose your preferred format

format_quote

Al-Quran, Ashraf, Ahmad, Abd Ghafur, Al-Sharqi, Faisal, Lutfi, Abdalwali. "Q-Complex Neutrosophic Set." International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 2, 2023, pp. 08-19. DOI: https://doi.org/10.54216/IJNS.200201

Al-Quran, A., Ahmad, A., Al-Sharqi, F., Lutfi, A. (2023). Q-Complex Neutrosophic Set. International Journal of Neutrosophic Science, Volume 20(Issue 2), 08-19. DOI: https://doi.org/10.54216/IJNS.200201

Al-Quran, Ashraf, Ahmad, Abd Ghafur, Al-Sharqi, Faisal, Lutfi, Abdalwali. "Q-Complex Neutrosophic Set." International Journal of Neutrosophic Science Volume 20, no. Issue 2 (2023): 08-19. DOI: https://doi.org/10.54216/IJNS.200201

Al-Quran, A., Ahmad, A., Al-Sharqi, F., Lutfi, A. (2023) 'Q-Complex Neutrosophic Set', International Journal of Neutrosophic Science, Volume 20(Issue 2), pp. 08-19. DOI: https://doi.org/10.54216/IJNS.200201

Al-Quran A, Ahmad A, Al-Sharqi F, Lutfi A. Q-Complex Neutrosophic Set. International Journal of Neutrosophic Science. 2023;Volume 20(Issue 2):08-19. DOI: https://doi.org/10.54216/IJNS.200201

A. Al-Quran, A. Ahmad, F. Al-Sharqi, A. Lutfi, "Q-Complex Neutrosophic Set," International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 2, pp. 08-19, 2023. DOI: https://doi.org/10.54216/IJNS.200201

Digital Archive Ready