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3. BMBJ-neutrosophic subalgebra in BCI/BCK-algebrasHashem 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: 1902; Downloads: 0
 Fulltext (251,21 KB) |
4. A GENERAL MODEL OF NEUTROSOPHIC IDEALS IN BCK/BCI-ALGEBRAS BASED ON NEUTROSOPHIC POINTSHashem 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: 1604; Downloads: 0
Fulltext (450,37 KB) |
5. Implicative falling neutrosophic ideals of BCK-algebrasRajab 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: 1277; Downloads: 0
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7. N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structuresYoung 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: 849; Downloads: 34
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8. Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadowsYoung Bae Jun, Rajab Ali Borzooei, Xiao Long Xin, Hashem Bordbar, 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.
Found in: osebi
Keywords: neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Published: 06.06.2022; Views: 565; Downloads: 0
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