A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty
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 w...
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doaj-3bbe01ca6b2743639f8af3177a0767f72020-11-25T03:21:46ZengMDPI AGSymmetry2073-89942019-03-0111338410.3390/sym11030384sym11030384A Novel Approach to Neutrosophic Soft Rough Set under UncertaintyAshraf Al-Quran0Nasruddin Hassan1Emad Marei2Department of Mathematics, Faculty of Science, Jerash University, Jerash 26150, JordanFaculty of Science and Technology, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, UKM Bangi Selangor 43600, DE, MalaysiaDepartment of Mathematics, Faculty of Science and Art, Shaqra University, Shaqra 11961, Saudi ArabiaTo 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.http://www.mdpi.com/2073-8994/11/3/384decision makingmembership functionneutrosophic setneutrosophic soft roughrelationsrough set approximationsoft set |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ashraf Al-Quran Nasruddin Hassan Emad Marei |
spellingShingle |
Ashraf Al-Quran Nasruddin Hassan Emad Marei A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty Symmetry decision making membership function neutrosophic set neutrosophic soft rough relations rough set approximation soft set |
author_facet |
Ashraf Al-Quran Nasruddin Hassan Emad Marei |
author_sort |
Ashraf Al-Quran |
title |
A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty |
title_short |
A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty |
title_full |
A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty |
title_fullStr |
A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty |
title_full_unstemmed |
A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty |
title_sort |
novel approach to neutrosophic soft rough set under uncertainty |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2019-03-01 |
description |
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. |
topic |
decision making membership function neutrosophic set neutrosophic soft rough relations rough set approximation soft set |
url |
http://www.mdpi.com/2073-8994/11/3/384 |
work_keys_str_mv |
AT ashrafalquran anovelapproachtoneutrosophicsoftroughsetunderuncertainty AT nasruddinhassan anovelapproachtoneutrosophicsoftroughsetunderuncertainty AT emadmarei anovelapproachtoneutrosophicsoftroughsetunderuncertainty AT ashrafalquran novelapproachtoneutrosophicsoftroughsetunderuncertainty AT nasruddinhassan novelapproachtoneutrosophicsoftroughsetunderuncertainty AT emadmarei novelapproachtoneutrosophicsoftroughsetunderuncertainty |
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