Next Article in Journal
Secrecy Performance of Underlay Cooperative Cognitive Network Using Non-Orthogonal Multiple Access with Opportunistic Relay Selection
Next Article in Special Issue
A Refined Approach for Forecasting Based on Neutrosophic Time Series
Previous Article in Journal
Pythagorean Fuzzy Dombi Aggregation Operators and Their Application in Decision Support System
Previous Article in Special Issue
Fuzzy Parameterized Complex Neutrosophic Soft Expert Set for Decision under Uncertainty
 
 
Article

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

1
Department of Mathematics, Faculty of Science, Jerash University, Jerash 26150, Jordan
2
Faculty of Science and Technology, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, UKM Bangi Selangor 43600, DE, Malaysia
3
Department of Mathematics, Faculty of Science and Art, Shaqra University, Shaqra 11961, Saudi Arabia
*
Author to whom correspondence should be addressed.
Deceased 13 July 2018.
Symmetry 2019, 11(3), 384; https://doi.org/10.3390/sym11030384
Received: 5 January 2019 / Revised: 20 February 2019 / Accepted: 25 February 2019 / Published: 15 March 2019
To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided. View Full-Text
Keywords: decision making; membership function; neutrosophic set; neutrosophic soft rough; relations; rough set approximation; soft set decision making; membership function; neutrosophic set; neutrosophic soft rough; relations; rough set approximation; soft set
MDPI and ACS Style

Al-Quran, A.; Hassan, N.; Marei, E. A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty. Symmetry 2019, 11, 384. https://doi.org/10.3390/sym11030384

AMA Style

Al-Quran A, Hassan N, Marei E. A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty. Symmetry. 2019; 11(3):384. https://doi.org/10.3390/sym11030384

Chicago/Turabian Style

Al-Quran, Ashraf, Nasruddin Hassan, and Emad Marei. 2019. "A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty" Symmetry 11, no. 3: 384. https://doi.org/10.3390/sym11030384

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop