Young Bae Jun (Author), Seok-Zun Song (Author), Florentin Smarandache (Author), Hashem Bordbar (Author)

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.

Keywords

neutrosophic quadruple BCK/BCI-number;neutrosophic quadruple BCK/BCI-algebra;neutrosophic quadruple subalgebra;neutrosophic quadruple ideal;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UNG - University of Nova Gorica
UDC: 512
COBISS: 5489403 Link will open in a new window
ISSN: 2075-1680
Views: 2242
Downloads: 0
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Other data

URN: URN:SI:UNG
Type (COBISS): Not categorized
Pages: str. 1-16
Volume: ǂVol. ǂ7
Issue: ǂiss. ǂ2
Chronology: 2018
DOI: 10.3390/axioms7020041
ID: 11314161