Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 28, Issue 11, Pages 2996-3007Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2019.2946526
Keywords
Multigranulation rough set; N-soft set; rough set; soft set; tolerance relation; tolerance rough set
Funding
- National Natural Science Foundation of China [51875457, 11301415]
- Natural Science Basic Research Plan in Shaanxi Province of China [2018JM1054]
- Scientific Research Program - Shaanxi Provincial Education Department of China [16JK1696]
- Special Funds Project for Key Disciplines Construction of Shaanxi Universities
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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.
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