Science Journal of Applied Mathematics and Statistics
Volume 7, Issue 6, December 2019, Pages: 95-102
Received: May 13, 2019;
Accepted: Oct. 4, 2019;
Published: Oct. 28, 2019
Views 346 Downloads 128
Somen Debnath, Department of Mathematics, Tripura University, Agartala, India
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.
About Rough Neutrosophic Soft Sets Theory and Study Their Properties, Science Journal of Applied Mathematics and Statistics.
Vol. 7, No. 6,
2019, pp. 95-102.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338-353.
W. L. Gau, D. J. Buehrer, Vague sets, IEEE Trans. Systems, Man, and Cybernetics, 23 (1993), 610-614.
J. Goguen, L fuzzy sets, Journal of Mathematical Analysis and Applications, 18 (1967), 145-174.
Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982) 341-356.
K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
M. Gorzalczany, A method of inference in approximate reasoning based on interval valued fuzzy sets, Fuzzy Sets and Systems, 21 (1987), 1-17.
K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31 (1989), 343-349.
D. Molodtsov, Soft set theory first results, Computers and Mathematics with Application, 37 (1999), 19-31.
P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, Journal of Fuzzy Mathematics, 9 (2001), 589-602.
P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 12 (2004), 669-683.
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.
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.
K. Moinuddin, Rough soft sets, International Journal of Computational and Applied Mathematics, 12 (2017), 537-543.
F. Smarandache, Neutrosophic set, International Journal of Pure and Applied Mathematics, 24 (2005), 287-297.
P. K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5 (2013), 157-168.