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Open AccessArticle

Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

1
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
2
Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
3
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
4
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(7), 296; https://doi.org/10.3390/sym10070296
Received: 28 June 2018 / Revised: 15 July 2018 / Accepted: 18 July 2018 / Published: 23 July 2018
It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility. View Full-Text
Keywords: neutrosophic rough set; MGNRS; dual domains; inclusion relation; decision-making neutrosophic rough set; MGNRS; dual domains; inclusion relation; decision-making
MDPI and ACS Style

Bo, C.; Zhang, X.; Shao, S.; Smarandache, F. Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications. Symmetry 2018, 10, 296.

AMA Style

Bo C, Zhang X, Shao S, Smarandache F. Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications. Symmetry. 2018; 10(7):296.

Chicago/Turabian Style

Bo, Chunxin; Zhang, Xiaohong; Shao, Songtao; Smarandache, Florentin. 2018. "Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications" Symmetry 10, no. 7: 296.

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