21. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation MapsHashem Bordbar, Young Bae Jun, Seok Zun Song, 2018, izvirni znanstveni članek Opis: 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.
Ključne besede: ideal, I-quasi-valuation map, I-valuation map, quasi-metric
Objavljeno v RUNG: 01.12.2019; Ogledov: 3823; Prenosov: 0
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23. Semiring structures based on meet and plus ideals in lower BCK-semilatticesHashem Bordbar, 2017, izvirni znanstveni članek Opis: The notion of the meet set based on two subsets of a lower BCK-semilattice X is introduced, and related properties are investigated. Conditions for the meet set to be a (positive implicative, commutative, implicative) ideal are discussed. The meet ideal based on subsets, and the plus ideal of two subsets in a lower BCK-semilattice X are also introduced, and related properties are investigated. Using the meet operation and addition, the semiring structure is induced.
Ključne besede: Lower BCK-semilattice, meet set, meet ideal, plus ideal, meet operation, addition, semiring.
Objavljeno v RUNG: 01.12.2019; Ogledov: 3660; Prenosov: 0
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24. Neutrosophic Quadruple BCK/BCI-AlgebrasYoung Bae Jun, Seok-zun Song, Florentin Smarandache, Hashem Bordbar, 2018, izvirni znanstveni članek Opis: 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.
Ključne besede: neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal
Objavljeno v RUNG: 01.12.2019; Ogledov: 4075; Prenosov: 0
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25. Relative annihilators in lower BCK-semilatticesHashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2017, izvirni znanstveni članek Opis: As a generalization of annihilators, the notion of a relative annihilator is introduced, and their properties are investigated. Conditions for a relative annihilator to be an implicative (resp., positive implicative, commutative) ideal are discussed.
Ključne besede: Lower BCK-semilattice, relative annihilator, implicative ideal, positive implicative ideal, commutative ideal
Objavljeno v RUNG: 01.12.2019; Ogledov: 3999; Prenosov: 0
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26. Further results on (∈, ∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebrasG Muhiuddin, Hashem Bordbar, Florentin Smarandache, Young Bae Jun, 2018, izvirni znanstveni članek Opis: Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The re- lation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and re- lated properties are investigated.
Ključne besede: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal.
Objavljeno v RUNG: 01.12.2019; Ogledov: 3898; Prenosov: 0
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