Hybrid bi-ideals in near-subtraction semigroups

Year 2024, Volume: 53 Issue: 5, 1250 - 1263, 15.10.2024

S. Meenakshi1 , G. Muhiuddin , Deena Al-kadi , B Elavarasan

https://doi.org/10.15672/hujms.1229332

Abstract

The fuzzy set is an excellent solution for dealing with ambiguity and for expressing people's hesitation in regular life. Soft set theory is an innovative method for solving practical issues. This is useful in resolving a number of problems, and a lot of progress is being made at the moment. In order to develop hybrid structures, Jun et al. fused the fuzzy and soft sets. In this paper, the notion of hybrid bi-ideals in near-subtraction semigroups is proposed and their associated results are discussed. The notion of hybrid intersections is examined. Furthermore, we establish some results related to the homomorphic preimage of a hybrid bi-ideal in near-subtraction semigroups.

Keywords

subtraction semigroup, bi-ideals, hybrid structure, hybrid intersection, hybrid bi-ideals

References

• [1] S. Anis, M. Khan and Y. B. Jun, Hybrid ideals in semigroups, Cogent Math. 4, 1352117, 2017.
• [2] V. Chinnadurai and S. Kadalarasi, Fuzzy bi-ideals of near-subtraction semigroups, Annals of Fuzzy Mathematics and Informatics 12(6), 781–790, 2016.
• [3] J. R. Clay, The near-rings on groups of low order, Math. Z. 104 (5), 364–371, 1968.
• [4] P. Dheena and B. Elavarasan, An ideal-based zero-divisor graph of 2-primal nearrings, Bull. Korean Math. Soc. 46(6), 1051–1060, 2009.
• [5] P. Dheena and G. Satheesh kumar, On storngly regular near-subtraction semigroups, Commun. Korean Math. Soc. 22(3), 323–330, 2007.
• [6] B. Elavarasan and Y. B. Jun, Regularity of semigroups in terms of hybrid ideals and hybrid bi-ideals, Kragujev. J. Math. 46(6), 857–864, 2022.
• [7] B. Elavarasan, G. Muhiuddin, K. Porselvi and Y. B. Jun, Hybrid structures applied to ideals in near-rings, Complex Intell. Syst. 7(3), 1489–1498, 2021.
• [8] B. Elavarasan, K. Porselvi and Y. B. Jun, Hybrid generalized bi-ideals in semigroups, Int. J. Math. Comput. Sci. 14(3), 601–612, 2019.
• [9] Y. B. Jun, H. S. Kim and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61(3), 459–464, 2005.
• [10] Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. 65(1), 129–134, 2007.
• [11] Y. B. Jun, M. Sapanci and M. A. Ozturk, Fuzzy ideals in Gamma near-rings, Tr. J. Math. 22, 449–459, 1998.
• [12] Y. B. Jun, S. Z. Song and G. Muhiuddin, Hybrid structures and applications, Annals of communications in Mathematics 1(1), 11–25, 2018.
• [13] K. J. Lee and C. H. Park, Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22(3), 359–363, 2007.
• [14] V. Mahalakshmi, S. Maharasi and S. Jayalakshmi, Bi-ideals in near- subtraction semigroup, Indian Advances in Algebra 6(1), 35–48, 2013.
• [15] T. Manikandan, Fuzzy bi-ideals of near-rings, J. Fuzzy Math. 17(3), 659–671, 2009.
• [16] G. Mason, Strongly regular near-rings, Proc. Edinb. Math. Soc. 23(1), 27–35, 1980.
• [17] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002.
• [18] S. Meenakshi, G. Muhiuddin, B. Elavarasan and D. Al-Kadi, Hybrid ideals in nearsubtraction semigroups, AIMS Mathematics 7(7), 13493–13507, 2022.
• [19] J. D. P. Meldrum, Varieties and d.g. near-rings, Proc. Edinb. Math. Soc. 17(3), 271–274, 1971.
• [20] D. Molodtsov, Soft set theory–first results, Comput. Math. Appl. 37, 19–31, 1999.
• [21] G. Muhiuddin, J. Catherine Grace John, B. Elavarasan, Y. B. Jun and K. Porselvi, Hybrid structures applied to modules over semirings, J. Intell. Fuzzy Syst. 42(3), 2521–2531, 2022.
• [22] G. Muhiuddin, J. Catherine Grace John, B. Elavarasan, K. Porselvi and D. Al- Kadi, Properties of k-hybrid ideals in ternary semiring, J. Intell. Fuzzy Syst. 42(6), 5799–5807, 2022.
• [23] G. Pilz, Near-rings, North-Holland, Amsterdam, 1983.
• [24] K. Porselvi and B. Elavarasan, On hybrid interior ideals in semigroups, Probl. Anal. Issues. Anal. 8(26)(3), 137–146, 2019.
• [25] K. Porselvi, B. Elavarasan and Y. B. Jun, Hybrid interior ideals in ordered semigroups, New Math. Nat. Comput. 18(1), 1–8, 2022.
• [26] K. Porselvi, G. Muhiuddin, B. Elavarasan and A. Assiry, Hybrid nil radical of a ring, Symmetry 14, 1367, 2022.
• [27] K. Porselvi, G. Muhiuddin, B. Elavarasan, Y. B. Jun and J. Catherine Grace John, Hybrid ideals in an AG-groupoid, New Math. Nat. Comput. 19(1), 289–305, 2023.
• [28] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35, 512–517, 1971.
• [29] B. M. Schein, Difference semigroups, Commun. Algebra. 20(8), 2153–2169, 1992.
• [30] D. R. P. Williams, Fuzzy ideals in near-subtraction semigroups, International scholarly and scientific research and innovation 2(7), 625–632, 2008.
• [31] L. A. Zadeh, Fuzzy sets, Inf. Control. 8, 338–353, 1965.
• [32] B. Zelinka, Subtraction semigroups, Math. Bohem. 120(4), 445–447, 1995.