### N-LEVEL AND N-UPPER LEVEL SOFT SETS

#### Abstract

In this paper, the concept of n-upper level soft set is introduced together with some of its properties. It is shown that some properties holding in n-level soft set do not hold in n-upper level soft set. It is further demonstrated that both the first and the second decomposition theorems fails in n-upper level soft set.

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Ali, M. I., Feng F., Liu X., Min. W. K. M. and Shabir M. (2009). On some new operations in soft set theory, Computers and Mathematics with Applications, Elsevier, 57, 1547-1553.

Alkhazaleh, S., Salleh, A. R. & Hassan, N. (2011). Soft Multisets Theory, Applied Mathematical Sciences, 5 (72) 3561 – 3573.

Babitha, K. V. & Sunil, J. J. (2013). On soft multi sets, Annals of Fuzzy Mathematics and Informatics, 5 (1) 35-44.

Blizard, W. D. (1991). The Development of Multiset Theory, Modern Logic, 1, 319-352.

Girish, K. P. and John, S. J. (2009). General relations between partially ordered multisets and their chains and antichains, Math. Commun. 14 (2) 193-206.

Ibrahim, A. M., Awolola, J. A. and Alkali, A. J. (2016). An extension of the concept of n-level sets to multisets, Annals of Fuzzy Mathematics and Informatics, 11 (6) 855-862.

Isah, A. I. & Tella, Y. (2015). The Concept of Multiset Category, British Journal of Mathematics & Computer Science, 9 (5) 427-437.

Isah, A. I. (2019). An Introduction of the Concept of n-level Soft set, ABACUS, (Mathematics Science Series), The Journal of Mathematical Association of Nigeria 46 (1) 628-634.

Jena, S. P., Ghosh, S. K. & Tripathy, B.K. (2001). On the theory of bags and lists, Information Science 132, 241-254.

Maji, P. K., Roy, A. R. & Biswas, R. (2002). An application of soft sets in a decision making problem, Computers Math. With Appl., l, 44, 1077-1083.

Majumdar, P. (2012). Soft Multisets, Jounal of Mathematics and Computer Science, 2 (6) 1700-1711.

Molodtsov, D. (1999). Soft set theory-First results, Computers and mathematics with applications, 37, 4/5, 19-31.

Nazmul, S . K., Majumdar, P. and Samanta, S . K. (2013). On Multisets and Multigroups, Annals of Fuzzy Mathematics and Informatics, 6 (3) 643-656.

Qin, K. and Hong, Z. (2010). On soft equality, Journal of Computational and Applied Mathematics, 234, 1347-1355.

Sezgin, A. & Atagun, A.O. (2011). On operations of soft sets, Computers and mathematics with applications, 60, 1840-1849.

Singh, D., Ibrahim, A. M., Yohanna, T. & Singh, J. N. (2007). An Overview of The Applications of Multisets, Novi Sad J. Math, 37, 2, 73-92.

Singh, D. and Isah, A. I. (2016). Mathematics of multisets: a unified approach, Afrika Matematika, Springer, 27, 1139–1146.

Tokat, D. & Osmanoglu, I. (2013). Connectedness on Soft Multi Topological Spaces, J. New Results Sci. 2, 8-18.

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