Some results on multigranulation neutrosophic rough sets on a single domain

Hu Zhao; Hong Ying Zhang

doi:10.3390/sym10090417

Some results on multigranulation neutrosophic rough sets on a single domain

Hu Zhao
, Hong Ying Zhang

School of Mathematics and Statistics

Xi'an Polytechnic University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Article number	417
Journal	Symmetry
Volume	10
Issue number	9
DOIs	https://doi.org/10.3390/sym10090417
State	Published - 19 Sep 2018

Keywords

Complete lattice
Neutrosophic rough set
Neutrosophic set
Pessimistic (optimistic) multigranulation neutrosophic approximation operators

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10.3390/sym10090417

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title = "Some results on multigranulation neutrosophic rough sets on a single domain",

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.",

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AU - Zhao, Hu

AU - Zhang, Hong Ying

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N2 - 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.

AB - 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.

KW - Complete lattice

KW - Neutrosophic rough set

KW - Neutrosophic set

KW - Pessimistic (optimistic) multigranulation neutrosophic approximation operators

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DO - 10.3390/sym10090417

M3 - 文章

AN - SCOPUS:85054420792

SN - 2073-8994

VL - 10

JO - Symmetry

JF - Symmetry

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ER -

Some results on multigranulation neutrosophic rough sets on a single domain

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