Study on the Algebraic Structure of Refined Neutrosophic Numbers
This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator ⊕ and multiplication operator ⊗ on refined neutrosophic numbers are p...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/954 |
| _version_ | 1818005503486197760 |
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| author | Qiaoyan Li Yingcang Ma Xiaohong Zhang Juanjuan Zhang |
| author_facet | Qiaoyan Li Yingcang Ma Xiaohong Zhang Juanjuan Zhang |
| author_sort | Qiaoyan Li |
| collection | DOAJ |
| description | This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator ⊕ and multiplication operator ⊗ on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given. |
| first_indexed | 2024-04-14T04:45:02Z |
| format | Article |
| id | doaj.art-e2fc9a44098c48edacdc581585187e57 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T04:45:02Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e2fc9a44098c48edacdc581585187e572022-12-22T02:11:29ZengMDPI AGSymmetry2073-89942019-07-0111895410.3390/sym11080954sym11080954Study on the Algebraic Structure of Refined Neutrosophic NumbersQiaoyan Li0Yingcang Ma1Xiaohong Zhang2Juanjuan Zhang3School of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaSchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaSchool of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaThis paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator ⊕ and multiplication operator ⊗ on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given.https://www.mdpi.com/2073-8994/11/8/954neutrosophic extended triplet groupneutrosophic quadruple numbersrefined neutrosophic numbersrefined neutrosophic quadruple numbersneutrosophic set |
| spellingShingle | Qiaoyan Li Yingcang Ma Xiaohong Zhang Juanjuan Zhang Study on the Algebraic Structure of Refined Neutrosophic Numbers Symmetry neutrosophic extended triplet group neutrosophic quadruple numbers refined neutrosophic numbers refined neutrosophic quadruple numbers neutrosophic set |
| title | Study on the Algebraic Structure of Refined Neutrosophic Numbers |
| title_full | Study on the Algebraic Structure of Refined Neutrosophic Numbers |
| title_fullStr | Study on the Algebraic Structure of Refined Neutrosophic Numbers |
| title_full_unstemmed | Study on the Algebraic Structure of Refined Neutrosophic Numbers |
| title_short | Study on the Algebraic Structure of Refined Neutrosophic Numbers |
| title_sort | study on the algebraic structure of refined neutrosophic numbers |
| topic | neutrosophic extended triplet group neutrosophic quadruple numbers refined neutrosophic numbers refined neutrosophic quadruple numbers neutrosophic set |
| url | https://www.mdpi.com/2073-8994/11/8/954 |
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