Abstract
In this note, we introduce (M, N)-soft intersection nearsemirings (abbreviate as (M, N)-SI-nearsemirings) by utilizing the intersection operation of sets. We study the set theoretic characteristics of (M, N)-Soft intersection nearsemirings with the effects of different types of sets operations. (M, N)-SI-subnearsemirings, (M, N)-SI-ideals, and (M, N)-SI-c-ideals are also introduced and discussed. Furthermore, we introduce the notions of (M, N)-α-inclusion, soft uni-int c-products, soft uni-int c-sums and study (M, N)-SI-nearsemirings by using these operations. We also inter-relate (M, N)-SI-nearsemirings and classical nearsemirings by utilizing (M, N)-α-inclusion.
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U. Acar, F. Koyuncu, and B. Tanay, “Soft sets and soft rings,” Comput. Math. Appl. 59, 3458–3463 (2010).
M. I. Ali, F. Feng, X. Liub, W. K. Minc, and M. Shabir, “On some new operations in soft set theory,” Comput. Math. Appl. 57, 1547–1553 (2009).
H. Aktaş, and N. Çağman, “Soft sets and soft groups,” Inform Sci. 177, 2726–2735 (2007).
N. Çağman, and S. Enginoğlu, “Soft set theory and uni–int decision making,” Eur. J. Oper. Res. 207, 848–855 (2010).
N. Çağman, F. Çitak, and H. Aktaş, “Soft int–group and its applications to group theory,” Neural Comput. Appl. 21, 151–158 (2012).
F. Çitak and N. Çağman, “Soft int–rings and its algebraic applications,” J. Intell. Fuzzy Syst. 28, 1225–1233 (2015).
F. Çitak and N. Çağman, “Soft k–int–ideals of semirings and its algebraic structures,” Ann. Fuzzy Math. Inform. 13, 531–538 (2017).
F. Feng, Y. B. Jun, and X. Zhao, “Soft semirings,” Comput. Math. Appl. 56, 2621–2628 (2008).
F. Hussain, M. Tahir, S. Abdullah, and N. Sadiq, “Quotient seminearrings,” Indian J. Sci. Technol. 9 (38), 1–7 (2016).
W. A. Khan and A. Rehman, “Soft nearsemirings” (submitted).
W. A. Khan and B. Davaz, “Soft int–nearsemirings and their algebraic applications” (submitted).
K. V. Krishna, “Near–semirings theory and application,” PhD Thesis (Ind. Inst. Technol. Delhi, New Delhi, India, 2005).
K. V. Krishna and N. Chatterjee, “A necessary condition to test the minimality of generalized linear sequential machines using the theory of near–semirings,” Algebra DiscreteMath. 3, 30–45 (2005).
X. Ma and J. Zhan, “Soft intersection h–ideals of hemiring and its applications,” Ital. J. PureAppl. Math. 32, 301–308 (2014).
X. Ma and J. Zhan, “Applications of a new soft set to h–hemiregular hemirings via (M,N) − SI − h–ideals,” J. Intell. Fuzzy Syst. 26, 2515–2525 (2014).
D. Molodtsov, “Soft set theory—first results,” Comput. Math. Appl. 37, 19–31 (1999).
A. Sezgin, A. O. Atagün, and E. Aygün, “A note on soft near–rings and idealistic soft near–rings,” Filomat. 25, 53–68 (2011).
A. Sezgin and A. O. Atagün, “On operations of soft sets,” Comput. Math. Appl. 61, 1457–1467 (2011).
A. Sezgin, A. O. Atagün, and N. Çağman, “Soft intersection near–rings with its applications,” Neural Comput. Appl. 21, 221–229 (2012).
A. Sezgin, N. Çağman, and A. O. Atagün, “A completely new view to the soft intersection rings via soft uni–int product,” Appl. Soft Comput. C 54, 366–392 (2017).
W. G. V. Hoorn, and B. V. Rootselaar, “Fundamental notions in the theory of seminearrings,” Compos. Math. 18, 65–78 (1967).
H. J. Weinert, “Semi–nearrings, semi–nearfields and their semigroup–theoretical background,” Semigroup Forum 24, 231–254 (1982).
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Khan, W.A., Davvaz, B. & Muhammad, A. (M, N)-Soft Intersection Nearsemirings and (M, N)-α-Inclusion Along with Its Algebraic Applications. Lobachevskii J Math 40, 67–78 (2019). https://doi.org/10.1134/S1995080219010098
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DOI: https://doi.org/10.1134/S1995080219010098