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1.
Further results on (∈, ∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebras
Hashem Bordbar, Florentin Smarandache, Young Bae Jun, G Muhiuddin, 2018, original scientific article

Abstract: 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.
Found in: osebi
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal.
Published: 01.12.2019; Views: 1822; Downloads: 0
.pdf Fulltext (6,02 MB)

2.
Neutrosophic Quadruple BCK/BCI-Algebras
Hashem Bordbar, Young Bae Jun, Florentin Smarandache, Seok-zun Song, 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.
Found in: osebi
Keywords: neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal
Published: 01.12.2019; Views: 1803; Downloads: 0
.pdf Fulltext (284,81 KB)

3.
Neutrosophic N-Structures Applied to BCK/BCI-Algebras
Jun young Bae, Florentin Smarandache, Hashem Bordbar, 2017, original scientific article

Abstract: Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic N-ideal to be a closed neutrosophic N-ideal are provided.
Found in: osebi
Keywords: neutrosophic N-structure, neutrosophic N-subalgebra, (closed) neutrosophic N-ideal
Published: 01.12.2019; Views: 1754; Downloads: 0
.pdf Fulltext (261,83 KB)

4.
Neutrosophic falling shadows applied to subalgebras and ideals in BCK/BCI-algebras
Hashem Bordbar, Florentin Smarandache, Young Bae Jun, 2018, original scientific article

Abstract: As a combination of neutrosophic set and falling shadow, neutrosophic falling shadow is introduced, and applied to BCK/BCI- algebras. Falling neutrosophic subalgebra and falling neutrosophic ideal in BCK/BCI-algebras are introduced, and related properties are investi- gated. Relations between falling neutrosophic subalgebra and falling neu- trosophic ideal are discussed. A characterization of falling neutrosophic ideal is established.
Found in: osebi
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, Neutro- sophic random set, Neutrosophic falling shadow, Falling neutrosophic subalgebra, Falling neutrosophic ideal.
Published: 02.12.2019; Views: 1594; Downloads: 0
.pdf Fulltext (324,41 KB)

5.
Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras
Hashem 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.
Found in: osebi
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, neutrosophic (anti-)permeable S-value, neutrosophic (anti-)permeable I-value, S-energetic set, I-energetic set
Published: 02.12.2019; Views: 1674; Downloads: 0
.pdf Fulltext (297,13 KB)

6.
A GENERAL MODEL OF NEUTROSOPHIC IDEALS IN BCK/BCI-ALGEBRAS BASED ON NEUTROSOPHIC POINTS
Hashem Bordbar, Rajab Ali Borzooei, Florentin Smarandache, Young Bae Jun, 2020, original scientific article

Abstract: More general form of (∈, ∈∨q)-neutrosophic ideal is introduced, and their prop- erties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ) )-neutrosophic ideal are discussed. Characterizations of (∈, ∈ ∨q(kT ,kI ,kF ) )-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an (∈, ∈∨q(kT ,kI,kF ))-neutrosophic ideal are displayed.
Found in: osebi
Keywords: Ideal, neutrosophic ∈-subset, neutrosophic qk-subset, neutrosophic ∈∨qk-subset, (∈, ∈ ∨q(kT, kI, kF ))-neutrosophic ideal.
Published: 31.08.2020; Views: 1314; Downloads: 0
.pdf Fulltext (450,37 KB)

7.
Implicative falling neutrosophic ideals of BCK-algebras
Rajab Ali Borzooei, Young Bae Jun, Florentin Smarandache, Hashem Bordbar, Xiao Long Xin, 2021, original scientific article

Abstract: The notions of an implicative (2; 2)-neutrosophic ideal and an implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of an implicative (2; 2)-neutrosophic ideal are considered, and relations between an implicative (2; 2)-neutrosophic ideal and an (2; 2)-neutrosophic ideal are discussed. Conditions for an (2; 2)-neutrosophic ideal to be an implicative (2; 2)-neutrosophic ideal are provided, and relations between an implicative (2; 2)-neutrosophic ideal, a falling neutrosophic ideal and an implicative falling neutrosophic ideal are studied. Conditions for a falling neutrosophic ideal to be implicative are provided. Relations between implicative falling neutrosophic ideal, commutative falling neutrosophic ideal and positive implicative falling neutrosophic ideal are discussed.
Found in: osebi
Keywords: neutrosophic random set, neutrosophic falling shadow, (positive implicative) (2, 2)-neutrosophic ideal, (positive implicative) falling neutrosophic ideal, (commutative) (2, 2)-neutrosophic ideal, (commutative) falling neutrosophic ideal
Published: 15.03.2021; Views: 968; Downloads: 0
.pdf Fulltext (325,52 KB)

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