1. Neutrosophic N-Structures Applied to BCK/BCI-AlgebrasJun 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: ključnih besedah
Summary of found: ...is discussed. The notions of a neutrosophic N- subalgebra and a (closed) neutrosophic N-ideal in a...
Keywords: neutrosophic N-structure, neutrosophic N-subalgebra, (closed) neutrosophic N-ideal
Published: 01.12.2019; Views: 2162; Downloads: 0
 Fulltext (261,83 KB) |
2. Further results on (∈, ∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebrasHashem 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: ključnih besedah
Summary of found: ...between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for...
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal.
Published: 01.12.2019; Views: 2246; Downloads: 0
Fulltext (6,02 MB) |
3. Neutrosophic Quadruple BCK/BCI-AlgebrasHashem 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: ključnih besedah
Summary of found: ... BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal...
Keywords: neutrosophic quadruple BCK/BCI-number, neutrosophic quadruple BCK/BCI-algebra, neutrosophic quadruple subalgebra, (positive implicative) neutrosophic quadruple ideal
Published: 01.12.2019; Views: 2237; Downloads: 0
Fulltext (284,81 KB) |
4. A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebrasHashem Bordbar, Young Bae Jun, Seok Zun Song, 2017, original scientific article Abstract: The concept of a hesitant union (
Found in: ključnih besedah
Summary of found: ...Hesitant union, ∪-hesitant fuzzy subalgebra, ∪-hesitant fuzzy ideal,...
Keywords: Hesitant union, ∪-hesitant fuzzy subalgebra, ∪-hesitant fuzzy ideal
Published: 01.12.2019; Views: 2349; Downloads: 0
Fulltext (89,38 KB) |
5. BMBJ-neutrosophic ideals in BCK/BCI-algebrasHashem 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: ključnih besedah
Summary of found: ...The concepts of a BMBJ-neutrosophic ◦- subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced,...
Keywords: MBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic ideal, BMBJ-neutrosophic ◦-subalgebra.
Published: 02.12.2019; Views: 2335; Downloads: 0
Fulltext (223,15 KB) |
6. A Generalization of Semidetached Subalgebras in BCK∕BCI-algebrasYoung Bae Jun, Mohammad Rahim Bordbar, Hashem Bordbar, 2019, original scientific article Abstract: Generalization of the paper [Y. B. Jun and S. Z. Song, Semidetached subalgebras in BCK∕BCI-algebras, to appear in Bulletin of the Korean Mathematical Society] is discussed. Several conditions for a semidetached structure in BCK∕BCI-algebras to be a semidetached subalgebra are provided. The concepts of (∈¯,∈¯∨qk¯)-fuzzy subalgebra, k-left (k-right) (qk,∈∨qk)-fuzzy subalgebra, (qk¯,∈¯∨qk¯)-fuzzy subalgebra and (∈¯∨qk¯,∈¯∨qk¯)-fuzzy subalgebra are introduced, and relative relations and properties are discussed.
Found in: ključnih besedah
Summary of found: ...B. Jun and S. Z. Song, Semidetached subalgebras in BCK∕BCI-algebras, to appear in Bulletin of...
Keywords: ð2, 2_qkÞ-fuzzy subalgebra, k-left (k-right) ðqk, 2_qkÞ-fuzzy subalgebra, ð 2 _ qk, 2 _ qk Þ-fuzzy subalgebra, semidetached structure, semidetached subalgebra.
Published: 02.12.2019; Views: 2091; Downloads: 0
Fulltext (190,65 KB) |
7. Neutrosophic falling shadows applied to subalgebras and ideals in BCK/BCI-algebrasHashem 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: ključnih besedah
Summary of found: ...and applied to BCK/BCI- algebras. Falling neutrosophic subalgebra and falling neutrosophic ideal in BCK/BCI-algebras are...
Keywords: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, Neutro- sophic random set, Neutrosophic falling shadow, Falling neutrosophic subalgebra, Falling neutrosophic ideal.
Published: 02.12.2019; Views: 1926; Downloads: 0
Fulltext (324,41 KB) |
8. Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-AlgebrasHashem 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: ključnih besedah
Summary of found: ...(∈,∈)-neutrosophic subalgebra, (∈,∈)-neutrosophic ideal, neutrosophic (anti-)permeable S-value, neutrosophic (...
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: 2106; Downloads: 0
Fulltext (297,13 KB) |
9. 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: ključnih besedah
Keywords: BMBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic S-extension.
Published: 24.02.2020; Views: 2003; Downloads: 0
Fulltext (251,21 KB) |
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