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1.
Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows
Hashem Bordbar, Xiao Long Xin, Rajab Ali Borzooei, Young Bae Jun, 2022, original scientific article

Abstract: Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, ”A” in relation to its opposite, ”Anti-A” and that which is not A, ”Non-A”, and that which is neither ”A” nor ”Anti-A”, denoted by ”Neut-A”. Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. In this article, we apply the notion of neutrosophic set theory to (positive implicative) ideals in BCK-algebras by using the concept of falling shadows. The notions of a positive implicative (∈, ∈)-neutrosophic ideal and a positive implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a positive implicative (∈, ∈)-neutrosophic ideal are considered, and relations between a positive implicative (∈, ∈)-neutrosophic ideal and an (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be a positive implicative (∈, ∈)-neutrosophic ideal are provided, and relations between a positive implicative (∈, ∈)-neutrosophic ideal, a falling neutrosophic ideal and a positive implicative falling neutrosophic ideal are studied. Conditions for a falling neutrosophic ideal to be positive implicative are provided.
Keywords: neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Published in RUNG: 06.06.2022; Views: 1251; Downloads: 0
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2.
N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structures
Hashem Bordbar, Mohammad Rahim Bordbar, Rajab Ali Borzooei, Young Bae Jun, 2021, original scientific article

Abstract: In the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37], Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization of fuzzy sets and interval-valued fuzzy sets and applied it to group theory. The aim of this manuscript is to study N-structures in BCK\BCI-algebras induced from hyperfuzzy structures.
Keywords: hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N-function
Published in RUNG: 03.11.2021; Views: 1466; Downloads: 42
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3.
Soft subalgebras and ideals of BCK/BCI-algebras based on N -structures
Elhan Hassani Sadrabadi, Hashem Bordbar, Rajab Ali Borzooei, Arsham Borumand Saeid, Young Bae Jun, 2021, original scientific article

Keywords: N-ideal of types, soft N-subalgebra, soft N-ideal
Published in RUNG: 23.08.2021; Views: 1548; Downloads: 0
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4.
Implicative falling neutrosophic ideals of BCK-algebras
Xiao Long Xin, Hashem Bordbar, Florentin Smarandache, Rajab Ali Borzooei, Young Bae Jun, 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.
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 in RUNG: 15.03.2021; Views: 1904; Downloads: 0
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5.
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.
Keywords: Ideal, neutrosophic ∈-subset, neutrosophic qk-subset, neutrosophic ∈∨qk-subset, (∈, ∈ ∨q(kT, kI, kF ))-neutrosophic ideal.
Published in RUNG: 31.08.2020; Views: 2175; Downloads: 0
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6.
BMBJ-neutrosophic subalgebra in BCI/BCK-algebras
Hashem Bordbar, 2020, original scientific article

Abstract: For the first time, Smarandache introduced neutrosophic sets which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. the notion of BMBJ-neutrosophic set and subalgebra, as a generalization of a neutrosophic set, is introduced, and it’s an application to BCI/BCK-algebras is investigated. The concept of BMBJ-neutrosophic subalgebras in BCI/BCK-algebras is introduced, and related properties are investigated. New BMBJ-neutrosophic subalgebra is established by using a BMBJ-neutrosophic subalgebra of a BCI/BCK-algebra. Also, a homomorphic (inverse) image of BMBJ-neutrosophic subalgebra and translation of BMBJ-neutrosophic subalgebra is investigated. In the end, we provided conditions for a BMBJ-neutrosophic set to be a BMBJ-neutrosophic subalgebra.
Keywords: BMBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic S-extension.
Published in RUNG: 24.02.2020; Views: 2545; Downloads: 0
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7.
BMBJ-neutrosophic ideals in BCK/BCI-algebras
Hashem Bordbar, Young Bae Jun, 2019, original scientific article

Abstract: The concepts of a BMBJ-neutrosophic ◦-subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic ◦-subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.
Keywords: MBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic ideal, BMBJ-neutrosophic ◦-subalgebra.
Published in RUNG: 02.12.2019; Views: 2860; Downloads: 0
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8.
Uni-Soft Commutative Ideals and Closed Uni-Soft Ideals in BCI-Algebras
Hashem Bordbar, Young Bae Jun, Rajab ali Borzooei, 2018, original scientific article

Abstract: The notions of uni-soft commutative ideals and closed uni-soft ideals in BCI-algebras are introduced, and related properties are investigated. Conditions for a uni-soft ideal to be closed are provided. Relations between a uni-soft ideal and a uni-soft commutative ideal are investigated. Conditions for a uni-soft ideal to be a uni-soft commutative ideal are provided. A new uni-soft commutative ideal from an old one is constructed.
Keywords: Exclusive set, (closed) uni-soft ideal, uni-soft commutative ideal.
Published in RUNG: 01.12.2019; Views: 2646; Downloads: 0
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