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1.
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.
Found in: osebi
Keywords: Exclusive set, (closed) uni-soft ideal, uni-soft commutative ideal.
Published: 01.12.2019; Views: 1552; Downloads: 0
.pdf Fulltext (291,26 KB)

2.
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.
Found in: osebi
Keywords: MBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic ideal, BMBJ-neutrosophic ◦-subalgebra.
Published: 02.12.2019; Views: 1756; Downloads: 0
.pdf Fulltext (223,15 KB)

3.
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.
Found in: osebi
Keywords: BMBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic S-extension.
Published: 24.02.2020; Views: 1481; Downloads: 0
.pdf Fulltext (251,21 KB)

4.
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: 1202; Downloads: 0
.pdf Fulltext (450,37 KB)

5.
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: 844; Downloads: 0
.pdf Fulltext (325,52 KB)

6.
7.
N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structures
Young Bae Jun, Rajab Ali Borzooei, Hashem Bordbar, Mohammad Rahim Bordbar, 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.
Found in: osebi
Keywords: hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N-function
Published: 03.11.2021; Views: 460; Downloads: 16
URL Fulltext (0,00 KB)
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