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.
F. Hussain, M. Tahir, S. Abdullah, and N. Sadiq, “Quotient seminearrings,” Indian J. Sci. Technol. 9 (38), 1–7 (2016).Google Scholar
W. A. Khan and A. Rehman, “Soft nearsemirings” (submitted).Google Scholar
W. A. Khan and B. Davaz, “Soft int–nearsemirings and their algebraic applications” (submitted).Google Scholar
K. V. Krishna, “Near–semirings theory and application,” PhD Thesis (Ind. Inst. Technol. Delhi, New Delhi, India, 2005).Google Scholar
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).MathSciNetzbMATHGoogle Scholar
X. Ma and J. Zhan, “Soft intersection h–ideals of hemiring and its applications,” Ital. J. PureAppl. Math. 32, 301–308 (2014).MathSciNetzbMATHGoogle Scholar
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).MathSciNetzbMATHGoogle Scholar