( M , N )-Soft Intersection Nearsemirings and ( M , N )- α -Inclusion Along with Its Algebraic Applications

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.