| Title: | Neutrosophic Quadruple BCK/BCI-Algebras |
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| Authors: | ID Jun, Young Bae (Author)
ID Song, Seok-zun (Author)
ID Smarandache, Florentin (Author)
ID Bordbar, Hashem (Author) |
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| Files: |
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UNG - University of Nova Gorica
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| Abstract: | The notion of a neutrosophic quadruple BCK/BCI number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B)
, which consists of neutrosophic quadruple BCK/BCI-numbers with a condition, is established. Conditions for the set NQ(A,B)
to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. An example to show that the set {0˜} is not a positive implicative ideal in a neutrosophic quadruple BCK-algebra is provided, and conditions for the set {0˜} to be a positive implicative ideal in a neutrosophic quadruple BCK-algebra are then discussed. |
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| Keywords: | neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal |
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| Publication version: | Version of Record |
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| Year of publishing: | 2018 |
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| Number of pages: | 16 |
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| Numbering: | 7 |
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| PID: | 20.500.12556/RUNG-4888-e5e4e0ec-f6fd-339d-6587-c64b9fce1253 |
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| COBISS.SI-ID: | 5489403 |
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| DOI: | https://doi.org/10.3390/axioms7020041 |
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| NUK URN: | URN:SI:UNG:REP:OK9MJRPR |
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| Publication date in RUNG: | 01.12.2019 |
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| Views: | 3003 |
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| Downloads: | 0 |
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