Single valued neutrosophic $ (m, n) $-ideals of ordered semirings

The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $ (m, n) $-ideals (SVN-$ (m, n) $-ideal...

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Published inAIMS mathematics Vol. 7; no. 1; pp. 1211 - 1223
Main Authors Al-Kaseasbeh, Saba, Tahan, Madeline Al, Davvaz, Bijan, Hariri, Mariam
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
(m，n)-ideal
ordered semiring
semiring
single valued neutrosophic (m，n)-ideal
single valued neutrosophic set
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022071

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Abstract The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $ (m, n) $-ideals (SVN-$ (m, n) $-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-$ (m, n) $-ideals under different operations of SVNS. Finally, we find a relationship between the $ (m, n) $-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring $ R $ to be an SVN-$ (m, n) $-ideal of $ R $.
AbstractList The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $ (m, n) $-ideals (SVN-$ (m, n) $-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-$ (m, n) $-ideals under different operations of SVNS. Finally, we find a relationship between the $ (m, n) $-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring $ R $ to be an SVN-$ (m, n) $-ideal of $ R $.
Author Hariri, Mariam
Al-Kaseasbeh, Saba
Davvaz, Bijan
Tahan, Madeline Al
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Cites_doi 10.1007/s40314-019-0930-5
10.12988/ams.2017.64115
10.1142/S0219498822501018
10.1007/978-3-319-14762-8
10.1016/S0165-0114(86)80034-3
10.1007/978-94-015-9964-1
10.1016/0165-0114(90)90025-2
10.5281/zenodo.3750220
10.1016/S0019-9958(65)90241-X
10.1080/00927872.2019.1710178
10.1016/j.fiae.2014.06.008
10.1155/2014/416530
10.1090/S0002-9904-1934-06003-8
10.54216/IJNS.0100201
10.1007/978-94-015-9333-5
10.5281/zenodo.3719350
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CorporateAuthor Department of Mathematics and Statistics, Zayed University, United Arab Emirates
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Tafila Technical University, Tafila, Jordan
Department of Mathematics, Lebanese International University, Lebanon
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SubjectTerms (m，n)-ideal
ordered semiring
semiring
single valued neutrosophic (m，n)-ideal
single valued neutrosophic set
Title Single valued neutrosophic $ (m, n) $-ideals of ordered semirings
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