About Rough Neutrosophic Soft Sets Theory and Study Their Properties

Somen Debnath

doi:doi:10.11648/j.sjams.20190706.11

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About Rough Neutrosophic Soft Sets Theory and Study Their Properties

Somen Debnath

Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 6)

Received: 13 May 2019 Accepted: 4 October 2019 Published: 28 October 2019

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Abstract

Earlier fuzzy set, vague set, intuitionistic fuzzy set, L fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 6)
DOI	10.11648/j.sjams.20190706.11
Page(s)	95-102
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Rough Set, Neutrosophic Set, Neutrosophic Soft Set

References

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[3]	J. Goguen, L fuzzy sets, Journal of Mathematical Analysis and Applications, 18 (1967), 145-174.
[4]	Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982) 341-356.
[5]	K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[6]	M. Gorzalczany, A method of inference in approximate reasoning based on interval valued fuzzy sets, Fuzzy Sets and Systems, 21 (1987), 1-17.
[7]	K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31 (1989), 343-349.
[8]	D. Molodtsov, Soft set theory first results, Computers and Mathematics with Application, 37 (1999), 19-31.
[9]	P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, Journal of Fuzzy Mathematics, 9 (2001), 589-602.
[10]	P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 12 (2004), 669-683.
[11]	B. Chetia, P. K. Das, An application of interval valued fuzzy soft sets in medical diagnosis, International Journal of Contemporary Mathematical Sciences, 5 (2010), 1887-1894.
[12]	Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tung, Interval valued intuitionistic fuzzy soft sets and their properties, Computers andMathematics with Applications, 60 (2010), 906-918.
[13]	K. Moinuddin, Rough soft sets, International Journal of Computational and Applied Mathematics, 12 (2017), 537-543.
[14]	F. Smarandache, Neutrosophic set, International Journal of Pure and Applied Mathematics, 24 (2005), 287-297.
[15]	P. K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5 (2013), 157-168.

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Somen Debnath. (2019). About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Science Journal of Applied Mathematics and Statistics, 7(6), 95-102. https://doi.org/10.11648/j.sjams.20190706.11

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Somen Debnath. About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Sci. J. Appl. Math. Stat. 2019, 7(6), 95-102. doi: 10.11648/j.sjams.20190706.11

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Somen Debnath. About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Sci J Appl Math Stat. 2019;7(6):95-102. doi: 10.11648/j.sjams.20190706.11

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@article{10.11648/j.sjams.20190706.11,
  author = {Somen Debnath},
  title = {About Rough Neutrosophic Soft Sets Theory and Study Their Properties},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {6},
  pages = {95-102},
  doi = {10.11648/j.sjams.20190706.11},
  url = {https://doi.org/10.11648/j.sjams.20190706.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190706.11},
  abstract = {Earlier fuzzy set, vague set, intuitionistic fuzzy set, L fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.},
 year = {2019}
}

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TY - JOUR
T1 - About Rough Neutrosophic Soft Sets Theory and Study Their Properties
AU - Somen Debnath
Y1 - 2019/10/28
PY - 2019
N1 - https://doi.org/10.11648/j.sjams.20190706.11
DO - 10.11648/j.sjams.20190706.11
T2 - Science Journal of Applied Mathematics and Statistics
JF - Science Journal of Applied Mathematics and Statistics
JO - Science Journal of Applied Mathematics and Statistics
SP - 95
EP - 102
PB - Science Publishing Group
SN - 2376-9513
UR - https://doi.org/10.11648/j.sjams.20190706.11
AB - Earlier fuzzy set, vague set, intuitionistic fuzzy set, L fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.
VL - 7
IS - 6
ER -

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Author Information

Somen Debnath

Department of Mathematics, Tripura University, Agartala, India

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APA Style

Somen Debnath. (2019). About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Science Journal of Applied Mathematics and Statistics, 7(6), 95-102. https://doi.org/10.11648/j.sjams.20190706.11

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ACS Style

Somen Debnath. About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Sci. J. Appl. Math. Stat. 2019, 7(6), 95-102. doi: 10.11648/j.sjams.20190706.11

Copy | Download

AMA Style

Somen Debnath. About Rough Neutrosophic Soft Sets Theory and Study Their Properties. Sci J Appl Math Stat. 2019;7(6):95-102. doi: 10.11648/j.sjams.20190706.11

Copy | Download

@article{10.11648/j.sjams.20190706.11,
  author = {Somen Debnath},
  title = {About Rough Neutrosophic Soft Sets Theory and Study Their Properties},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {6},
  pages = {95-102},
  doi = {10.11648/j.sjams.20190706.11},
  url = {https://doi.org/10.11648/j.sjams.20190706.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190706.11},
  abstract = {Earlier fuzzy set, vague set, intuitionistic fuzzy set, L fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.},
 year = {2019}
}

Copy | Download