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1.
ŁUKASIEWICZ ANTI FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS
Jeong Gi Kang, Hashem Bordbar, 2025, izvirni znanstveni članek

Opis: Abstract. The subalgebra of BCK/BCI-algebra using Łukasiewicz anti fuzzy set introduced by Jun is studied in this article. The concept of Łukasiewicz anti fuzzy subalgebra of a BCK/BCI-algebra is introduced, and several properties are investigated. The relationship between anti fuzzy subalgebra and Łukasiewicz anti fuzzy subalgebra is given, and the characterization of a Łukasiewicz anti fuzzy subalgebra is discussed. Conditions are found in which a Lukasiewicz anti fuzzy set is a Lukasiewicz anti fuzzy subalgebra Finally, conditions under which ⋖-subset, Υ- subset, and anti-subset become subalgebra are explored.
Ključne besede: Anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy subalgebra, ⋖-subset, Υ-subset, anti subset
Objavljeno v RUNG: 20.02.2023; Ogledov: 1046; Prenosov: 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, izvirni znanstveni članek

Opis: 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.
Ključne besede: hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N-function
Objavljeno v RUNG: 03.11.2021; Ogledov: 1751; Prenosov: 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, izvirni znanstveni članek

Ključne besede: N-ideal of types, soft N-subalgebra, soft N-ideal
Objavljeno v RUNG: 23.08.2021; Ogledov: 1838; Prenosov: 0
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4.
Internal and external cubic subalgebras of BCK/BCI-algebras
Hashem Bordbar, Mohammad Mehdi Zahedi, Young Bae Jun, 2021, izvirni znanstveni članek

Opis: A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK\BCI-algebra, and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal and external cubic subalgebras in BCK=BCI-algebra are discussed.
Ključne besede: subalgebra, internal cubic subalgebra, external cubic subalgebra
Objavljeno v RUNG: 07.04.2021; Ogledov: 2031; Prenosov: 0
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5.
FURTHER RESULTS ON LENGTH FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS
Hashem Bordbar, 2018, izvirni znanstveni članek

Ključne besede: hyperfuzzy set, hyperfuzzy subalgebra, length of hyperfuzzy set, length fuzzy subalgebra.
Objavljeno v RUNG: 06.01.2021; Ogledov: 2354; Prenosov: 0
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6.
BMBJ-neutrosophic subalgebra in BCI/BCK-algebras
Hashem Bordbar, 2020, izvirni znanstveni članek

Opis: 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.
Ključne besede: BMBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic S-extension.
Objavljeno v RUNG: 24.02.2020; Ogledov: 2836; Prenosov: 0
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7.
Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-Algebras
Hashem Bordbar, Young Bae Jun, Florentin Smarandache, Seok Zun Song, 2018, izvirni znanstveni članek

Opis: 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.
Ključne besede: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, neutrosophic (anti-)permeable S-value, neutrosophic (anti-)permeable I-value, S-energetic set, I-energetic set
Objavljeno v RUNG: 02.12.2019; Ogledov: 2934; Prenosov: 0
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8.
Neutrosophic falling shadows applied to subalgebras and ideals in BCK/BCI-algebras
Hashem Bordbar, Florentin Smarandache, Young Bae Jun, 2018, izvirni znanstveni članek

Opis: 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.
Ključne besede: (∈, ∈)-neutrosophic subalgebra, (∈, ∈)-neutrosophic ideal, Neutro- sophic random set, Neutrosophic falling shadow, Falling neutrosophic subalgebra, Falling neutrosophic ideal.
Objavljeno v RUNG: 02.12.2019; Ogledov: 2734; Prenosov: 0
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9.
A Generalization of Semidetached Subalgebras in BCK∕BCI-algebras
Hashem Bordbar, Mohammad Rahim Bordbar, Young Bae Jun, 2019, izvirni znanstveni članek

Opis: 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.
Ključne besede: 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.
Objavljeno v RUNG: 02.12.2019; Ogledov: 2928; Prenosov: 0
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10.
BMBJ-neutrosophic ideals in BCK/BCI-algebras
Hashem Bordbar, Young Bae Jun, 2019, izvirni znanstveni članek

Opis: 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.
Ključne besede: MBJ-neutrosophic set, BMBJ-neutrosophic subalgebra, BMBJ-neutrosophic ideal, BMBJ-neutrosophic ◦-subalgebra.
Objavljeno v RUNG: 02.12.2019; Ogledov: 3161; Prenosov: 0
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