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Neutrosophic Quadruple BCK/BCI-Algebras

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 18 Jun 2018 Slovenia English Publisher:MDPI AGJournal:Axioms, volume 7, page 41 (eissn: 2075-1680, Copyright policy )
Authors: Young Bae Jun; Seok-Zun Song; Florentin Smarandache; Hashem Bordbar;

doi: 10.3390/axioms7020041 , 10.5281/zenodo.1410851 , 10.5281/zenodo.2862226 , 10.5281/zenodo.1410850 , 10.6084/m9.figshare.7048454 , 10.6084/m9.figshare.7048454.v1 , 10.5281/zenodo.2862227

handle: 20.500.12556/RUNG-4888-e5e4e0ec-f6fd-339d-6587-c64b9fce1253

Neutrosophic Quadruple BCK/BCI-Algebras

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-algebra, neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple subalgebra, QA1-939, (positive implicative) neutrosophic quadruple ideal, Mathematics

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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
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