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Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

1
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 417; https://doi.org/10.3390/sym10090417
Received: 11 August 2018 / Revised: 10 September 2018 / Accepted: 13 September 2018 / Published: 19 September 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved. View Full-Text
Keywords: neutrosophic set; neutrosophic rough set; pessimistic (optimistic) multigranulation neutrosophic approximation operators; complete lattice neutrosophic set; neutrosophic rough set; pessimistic (optimistic) multigranulation neutrosophic approximation operators; complete lattice
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Zhao, H.; Zhang, H.-Y. Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain. Symmetry 2018, 10, 417.

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