An $N$-Soft Set Approach to Rough Sets

The philosophy of soft sets is founded on the fundamental idea of parameterization, while Pawlak's rough sets put more emphasis on the importance of granulation. As a multivalued extension of soft sets, the newly emerging concept called N-soft sets can provide a finer granular structure with higher distinguishable power. This article offers a fresh insight into rough set theory from the perspective of N-soft sets. We reveal a close connection between N-soft sets and rough structures of various types. First, we show how the corresponding structures of Pawlak's rough sets, tolerance rough sets, and multigranulation rough sets can be derived from a given N-soft set. Conversely, we investigate the representation of these distinct rough structures using the corresponding notions derived from suitable N-soft sets. The applicability of these theoretical results is highlighted with a case study using real data regarding hotel rating. The established two-way correspondences between N-soft sets and diverse rough structures are constructive, which can bridge the gap between seemingly disconnected disciplines and hopefully nourish the development of both rough sets and soft sets.