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Algebraic structures of soft sets associated with new operations. (English) Zbl 1221.03056

Summary: Recently, new operations have been defined for soft sets. We study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. Finally, we show that soft sets with a fixed set of parameters are MV-algebras and BCK-algebras.

MSC:

03E72 Theory of fuzzy sets, etc.
06D35 MV-algebras
06F35 BCK-algebras, BCI-algebras
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