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
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
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.
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Keywords:
neutrosophic rough set; MGNRS; dual domains; inclusion relation; decision-making
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleBo, 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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