1
Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, 83125,Indonesia
(mamika@unram.ac.id)
2
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
(aalquran@kfu.edu.sa)
3
Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq; College of Engineering, National University of Science and Technology, Dhi Qar, Iraq
(faisal.ghazi@uoanbar.edu.iq)
4
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), Kelantan Branch, 18500 Machang, Kelantan, Malaysia
(nhashima@tmsk.uitm.edu.my)
5
Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia; MEU Research Unit, Middle East University, Amman, 11831, Jordan; Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
(aalkhassawneh@kfu.edu.sa)
Abstract :
In this paper, our aim is to investigate the algebraic structures within the Q-complex neutrosophic soft model. We introduce two fundamental concepts: the Q-complex neutrosophic soft ring (Q-CNSR) and the Q-complex neutrosophic soft ideal (Q-CNSI). Q-CNSRs combine the properties of Q-complex neutrosophic soft sets (Q-CNSSs) with ring theory, effectively capturing uncertainty and indeterminacy present in ring operations through the incorporation of Q-complex neutrosophic membership values. Additionally, we define Q-CNSIs as subsets of Q-CNSRs that possess distinctive properties and hold significant roles in ring theory. Furthermore, we discuss and verify the specific algebraic properties of Q-CNSR and Q-CNSI. By examining these properties, we gain a deeper understanding of the algebraic behavior of Q-CNSR and Q-CNSI. In particular, we shed light on the relationship between Q-CNSRs and soft rings. This provides insights into how Q-CNSR relates to the broader framework of soft ring, highlighting the unique features and contributions of Q-complex neutrosophic soft structures in the realm of algebraic analysis. We have also verified the relations between Q-CNSR and Q-neutrosophic soft ring (Q-NSR), as well as between Q-CNSI and Q-neutrosophic soft ideal (Q-NSI). Through this comprehensive exploration, our objective is to advance the understanding of Q-CNSR and Q-CNSI, thereby contributing to the field of algebraic analysis and its application in handling uncertainty and vagueness.
Keywords :
Complex neutrosophic soft set; Q-complex neutrosophic soft set; Q-neutrosophic soft ideal; Qneutrosophic soft ring; Q-neutrosophic soft set.
References :
[1] F. Smarandache, Neutrosophic probability, set, and logic, American Research Press: Rehoboth, IL, USA, 1998.
[2] D. Molodtsov, Soft set theory, first results, Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[3] Al-Jumaili, A. F.; Abed, M.M.; Al-Sharqi, F. Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ − β − θ-open sets. Journal of Physics: Conference Series, 2019, 1234(1), 012101.
[4] Z. bin M. Rodzi et al., “Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia,” Int. J. Neutrosophic Sci., vol. 21, no. 3, pp. 106–114, 2023.
[5] S. H. Zail, M. M. Abed and F. Al-Sharqi, (2022). Neutrosophic BCK-algebra and -BCK-algebra. International Journal of Neutrosophic Science, 19(3), 8-15.
[6] F. Al-Sharqi, A. Al-Quran, M. U. Romdhini, Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment, Iraqi Journal for Computer Science and Mathematics, vol. 4, pp.18–29, 2023.
[7] F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1) (2023), 358-382.
[8] A. Al-Quran, F. Al-Sharqi, K. Ullah, M. U. Romdhini, M. Balti and M. Alomai, Bipolar fuzzy hypersoft set and its application in decision making, International Journal of Neutrosophic Science, vol. 20, no. 4, pp. 65-77, 2023.
[9] M. U. Romdhini, F. Al-Sharqi, A. Nawawi, A. Al-Quran and H. Rashmanlou, Signless Laplacian Energy of Interval-Valued Fuzzy Graph and its Applications, Sains Malaysiana 52(7), 2127-2137, 2023.
[10] F. Al-Sharqi, A. G. Ahmad, A. Al Quran, Mapping on interval complex neutrosophic soft sets, International Journal of Neutrosophic Science, vol.19(4), pp.77-85, 2022.
[11] Mohammed Alqarni, Ahmed H. Samak, Safaa S. I. Ismail, Rasha M. Abd El-Aziz, Ahmed I. Taloba. (2023). Utilizing a Neutrosophic Fuzzy Logic System with ANN for Short-Term Estimation of Solar Energy. International Journal of Neutrosophic Science, 20 ( 4 ), 240-259.
[12] Abed, M. M., Al-Sharqi, F., & Zail, S. H. (2021, March). A Certain Conditions on Some Rings Give PP Ring. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012068). IOP Publishing.
[13] M Palanikumar, N Kausar, H Garg, SF Ahmed, C Samaniego, Robot sensors process based on generalized Fermatean normal different aggregation operators framework, AIMS Mathematics 8 (7), 16252- 16277, 2023.
[14] Broumi, S., Sundareswaran, R., Shanmugapriya, M., Bakali, A., Talea, M. (2022). Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets and Systems, 50, 248-286.
[15] F. Al-Sharqi, M. U. Romdhini, A. Al-Quran, Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, vol. 45, pp.305–321, 2023.
[16] 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(1), pp. 267–293, 2022.
[17] Al-Sharqi, F. G., Abed, M. M., Mhassin, A. A. On Polish Groups and their Applications. J. Eng. Appl. Sci., 2018, 13(18), 7533-7536.
[18] F. Al-Sharqi, A.G. Ahmad, and A. Al-Quran, Similarity measures on interval-complex neutrosophic soft sets with applications to decision making and medical diagnosis under uncertainty, Neutrosophic Setsand Systems, vol. 51, pp.495–515, 2022.
[19] Broumi, S., Mohanaselvi, S., Witczak, T., Talea, M., Bakali, A., Smarandache, F. (2023). Complex fermatean neutrosophic graph and application to decision making. Decision Making: Applications in Management and Engineering, 6(1), 474-501.
[20] M. Ali, F. Smarandache, Complex neutrosophic set, Neural Computing and Applications, vol.28 , pp. 1817-1834, 2017.
[21] S. Broumi, A. Bakali, F. Smarandache, M. Talea, M. Ali, G. Selvachandran, Complex neutrosophic soft set. FUZZ-IEEE Conference on Fuzzy Systems, 2017.
[22] Broumi, S., Raut, P. K., Behera, S. P. (2023). Solving shortest path problems using an ant colony algorithm with triangular neutrosophic arc weights. International Journal of Neutrosophic Science, 20(4), 128-28.
[23] M. Abu Qamar and N. Hassan, An approach toward a Q-neutrosophic soft set and its application in decision making, Symmetry, vol. 11, pp. 139, 2019.
[24] M. O. Alsarahead and A. G. Ahmad, Complex fuzzy subgroups, Applied Mathematical Sciences, vol. 11, pp. 2011 - 2021, 2017.
[25] M. O. Alsarahead and A. G. Ahmad, Complex fuzzy subrings, International Journal of Pure and Applied Mathematics, vol. 117, pp. 563 - 577, 2017.
[26] M. O. Alsarahead and A. G. Ahmad, Complex fuzzy soft rings, Palestine Journal of Mathematics, vol. 9, pp. 289 - 298, 2020.
[27] M. O. Alsarahead and A. G. Ahmad, Complex intuitionistic fuzzy subrings, Borneo Science, vol. 38,
2017. DOI: https://doi.org/10.51200/bsj.v38i2.4413
[28] M. O. Alsarahead and A. G. Ahmad, Complex intuitionistic fuzzy ideals, AIP Conference Proceedings , vol. 1940(1):020118, 2017. DOI: 10.1063/1.5028033.
[29] A. Al Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, vol. 20(2), pp.08-19, 2023.
[30] Ashraf Al-Quran, Faisal Al-Sharqi, Zahari Md. Rodzi, Mona Aladil, Rawan A. shlaka, Mamika Ujianita Romdhini, Mohammad K. Tahat, Obadah Said Solaiman. (2023). The Algebraic Structures of QComplex Neutrosophic Soft Sets Associated with Groups and Subgroups. International Journal of Neutrosophic Science, 22 ( 1 ), 60-76.
| Style | # |
|---|---|
| MLA | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi. "Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings." International Journal of Neutrosophic Science, Vol. 22, No. 4, 2023 ,PP. 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |
| APA | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi. (2023). Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |
| Chicago | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi. "Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings." Journal of International Journal of Neutrosophic Science, 22 no. 4 (2023): 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |
| Harvard | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi. (2023). Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |
| Vancouver | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi. Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 4 ): 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |
| IEEE | Mamika Ujianita Romdhini, Ashraf Al-Quran, Faisal Al-Sharqi, Hazwani Hashim, Abdalwali Lutfi, Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 4 , (2023) : 29-35 (Doi : https://doi.org/10.54216/IJNS.220402) |