11. Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-AlgebrasHashem Bordbar, Young Bae Jun, Florentin Smarandache, Seok Zun Song, 2018, original scientific article Abstract: The concept of a (∈, ∈)-neutrosophic ideal is introduced, and its characterizations are established. The notions of neutrosophic permeable values are introduced, and related properties are investigated. Conditions for the neutrosophic level sets to be energetic, right stable, and right vanished are discussed. Relations between neutrosophic permeable S- and I-values are considered.
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, neutrosophic (anti-)permeable S-value, neutrosophic (anti-)permeable I-value, S-energetic set, I-energetic set
Published in RUNG: 02.12.2019; Views: 2840; Downloads: 0
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12. Tender and naive weak closure operations on lower BCK-semilattices.Hashem Bordbar, 2018, original scientific article Abstract: The notion of tender and naive weak closure operation is introduced, and their relations and properties are investigated. Using a weak closure operation "d" and an ideal A of a lower BCK-semilattice X with the greatest element 1, a new ideal K of X containing the ideal Acl of X is established. Using this ideal K, a new function clt : I(X) → I(X); A → K is given, and related properties are considered. We show that if "cl" is a tender (resp., naive) weak closure operation on I(X), then so are "clt" and clf.
Keywords: zeromeet element, meet ideal, relative annihilator, (finite type, tender, naive) weak closure operation.
Published in RUNG: 02.12.2019; Views: 2814; Downloads: 0
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14. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation MapsHashem Bordbar, Young Bae Jun, Seok Zun Song, 2018, original scientific article Abstract: Relations between I-quasi-valuation maps and ideals in BCK/BCI
-algebras are investigated. Using the notion of an I-quasi-valuation map of a BCK/BCI-algebra, the quasi-metric space is induced, and several properties are investigated. Relations between the I-quasi-valuation map and the I-valuation map are considered, and conditions for an I-quasi-valuation map to be an I-valuation map are provided. A congruence relation is introduced by using the I-valuation map, and then the quotient structures are established and related properties are investigated. Isomorphic quotient BCK/BCI-algebras are discussed.
Keywords: ideal, I-quasi-valuation map, I-valuation map, quasi-metric
Published in RUNG: 01.12.2019; Views: 2803; Downloads: 0
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16. Neutrosophic Quadruple BCK/BCI-AlgebrasYoung Bae Jun, Seok-zun Song, Florentin Smarandache, Hashem Bordbar, 2018, original scientific article 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, (positive implicative) neutrosophic quadruple ideal
Published in RUNG: 01.12.2019; Views: 3056; Downloads: 0
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19. Tracking of urban aerosols using a scanning Mie lidarTingyao He, Fei Gao, Samo Stanič, Klemen Bergant, Darko Veberič, Xiaoquan Song, Aleš Dolžan, 2011, published scientific conference contribution abstract Keywords: aerosoli, mesta, lidar, okoljski monitoring
Published in RUNG: 15.10.2013; Views: 7619; Downloads: 147
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