The goal of this paper is to create an algebraic structure based on single-valued neutrosophic sets. We present a novel approach to the neutrosophic sub-ring and ideal by combining the classical ring with neutrosophic sets. We also introduce and investigate some of the fundamental properties of the concepts. Finally, we show how to use a neutrosophic ideal to make a decision.
Citation: Amr Elrawy, Mohamed Abdalla. Results on a neutrosophic sub-rings[J]. AIMS Mathematics, 2023, 8(9): 21393-21405. doi: 10.3934/math.20231090
The goal of this paper is to create an algebraic structure based on single-valued neutrosophic sets. We present a novel approach to the neutrosophic sub-ring and ideal by combining the classical ring with neutrosophic sets. We also introduce and investigate some of the fundamental properties of the concepts. Finally, we show how to use a neutrosophic ideal to make a decision.
| [1] | A. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. |
| [2] |
M. A. Basset, R. Mohamed, A. E. N. H. Zaied, F. Smarandache, A hybrid plithogenic decision-making approach with quality function deployment for selecting supply string sustainability metrics, Symmetry, 11 (2019), 903. https://doi.org/10.3390/sym11070903 doi: 10.3390/sym11070903
|
| [3] |
M. A. Basset, A. Atef, F. Smarandache, A hybrid Neutrosophic multiple criteria group decision making approach for project selection, Cogn. Syst. Res., 57 (2019), 216–227. https://doi.org/10.1016/j.cogsys.2018.10.023 doi: 10.1016/j.cogsys.2018.10.023
|
| [4] | A. A. A. Agboola, S. A. Akinleye, Neutrosophic vector spaces, Neutrosophic Sets Sy., 4 (2014), 9–18. |
| [5] |
S. Biswas, S. Moi, S. P. Sarkar, Neutrosophic riemann integration and its properties, Soft Comput., 25 (2021), 13987–13999. https://doi.org/10.1007/s00500-021-06200-7 doi: 10.1007/s00500-021-06200-7
|
| [6] |
V. Cetkin, H. Aygün, An approach to neutrosophic sub-ring, Sakarya U. J. Sci., 23 (2019), 472–477. https://doi.org/10.16984/saufenbilder.451979 doi: 10.16984/saufenbilder.451979
|
| [7] |
P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264–269. https://doi.org/10.1016/0022-247X(81)90164-5 doi: 10.1016/0022-247X(81)90164-5
|
| [8] | A. Elrawy, The neutrosophic vector spaces-another approach, Neutrosophic Set. Sy., 51 (2022), 484–494. |
| [9] | Elrawy, M. Abdalla, M. A. Saleem, Another approach to neutrosophic group, J. Math., 2023. |
| [10] | W. V. Kandasamy, F. Smarandache, Basic neutrosophic algebraic structures and their application to fuzzy and neutrosophic models, Infinite Study, 2004. |
| [11] | W. V. Kandasamy, F. Smarandache, Some neutrosophic algebraic structures and neutrosophic n-algebraic structures, Infinite Study, 2006. |
| [12] |
W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Set. Syst., 8 (1982), 133–139. https://doi.org/10.1016/0165-0114(82)90003-3 doi: 10.1016/0165-0114(82)90003-3
|
| [13] | S. Omran, A. Elrawy, Continuous and bounded operators on neutrosophic normed spaces, Neutrosophic Set. Sy., 46 (2021), 276–289. |
| [14] |
Y. T. Oyebo, Neutrosophic groups and subgroups, Math. Comb., 3 (2012), 1–9. https://doi.org/10.4310/JOC.2012.v3.n1.a1 doi: 10.4310/JOC.2012.v3.n1.a1
|
| [15] |
M. A. Saleem, M. Abdalla, A. Elrawy, On a matrix over NC and multiset NC semigroups, J. Math., 2022 (2022). https://doi.org/10.1155/2022/8095073 doi: 10.1155/2022/8095073
|
| [16] |
S. Siddique, U. Ahmad, M. Akram, A study on generalized graphs representations of complex neutrosophic information, J. Appl. Math. Comput., 65 (2021), 481–514. https://doi.org/10.1007/s12190-020-01400-0 doi: 10.1007/s12190-020-01400-0
|
| [17] | F. Smarandache, Neutrosophy: Neutrosophic probability, set, and logic: Analytic synthesis & synthetic analysis, Rehoboth, NM: American Research Press, 1998. |
| [18] | F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287. |
| [19] | F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, IEEE International Conference on Granular Computing, 2006. |
| [20] | F. Smarandache, Neutrosophic perspectives: Triplets, duplets, multisets, hybrid operators, modal logic, hedge algebras, and applications, Infinite Study, 2017. |
| [21] | H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Infinite Study, 2010. |
| [22] | L. A. Zadeh, Fuzzy sets, fuzzy logic, and fuzzy systems: Selected papers, 1996. |
| [23] | X. Zhang, C. Bo, F. Smarandache, J. Dai, New inclusion relation of neutrosophic sets with applications and related lattice structure, Int. J. Mach. Lear. Cyb., 9 (2018), 1753–1763. |
Amr Elrawy, Mohamed Abdalla. Results on a neutrosophic sub-rings[J]. AIMS Mathematics, 2023, 8(9): 21393-21405. doi: 10.3934/math.20231090
DownLoad: