New Multigranulation Neutrosophic Rough Set 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, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 578; https://doi.org/10.3390/sym10110578
Received: 3 September 2018 / Revised: 25 September 2018 / Accepted: 6 October 2018 / Published: 2 November 2018
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
After the neutrosophic set (NS) was proposed, NS was used in many uncertainty problems. The single-valued neutrosophic set (SVNS) is a special case of NS that can be used to solve real-word problems. This paper mainly studies multigranulation neutrosophic rough sets (MNRSs) and their applications in multi-attribute group decision-making. Firstly, the existing definition of neutrosophic rough set (we call it type-I neutrosophic rough set (NRSI) in this paper) is analyzed, and then the definition of type-II neutrosophic rough set (NRSII), which is similar to NRSI, is given and its properties are studied. Secondly, a type-III neutrosophic rough set (NRSIII) is proposed and its differences from NRSI and NRSII are provided. Thirdly, single granulation NRSs are extended to multigranulation NRSs, and the type-I multigranulation neutrosophic rough set (MNRSI) is studied. The type-II multigranulation neutrosophic rough set (MNRSII) and type-III multigranulation neutrosophic rough set (MNRSIII) are proposed and their different properties are outlined. We found that the three kinds of MNRSs generate tcorresponding NRSs when all the NRs are the same. Finally, MNRSIII in two universes is proposed and an algorithm for decision-making based on MNRSIII is provided. A car ranking example is studied to explain the application of the proposed model.
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Keywords:
inclusion relation; neutrosophic rough set; multi-attribute group decision-making (MAGDM); multigranulation neutrosophic rough set (MNRS); two universes
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. New Multigranulation Neutrosophic Rough Set with Applications. Symmetry 2018, 10, 578.
AMA Style
Bo C, Zhang X, Shao S, Smarandache F. New Multigranulation Neutrosophic Rough Set with Applications. Symmetry. 2018; 10(11):578.
Chicago/Turabian StyleBo, Chunxin; Zhang, Xiaohong; Shao, Songtao; Smarandache, Florentin. 2018. "New Multigranulation Neutrosophic Rough Set with Applications" Symmetry 10, no. 11: 578.
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