1. SBE-algebras via intuitionistic fuzzy structuresTahsin Oner, Hashem Bordbar, Neelamegarajan Rajesh, Akbar Rezaei, 2024, izvirni znanstveni članek Opis: The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understanding the behavior of intuitionistic fuzzy logic in this algebraic structure. The study further establishes a bidirectional relationship between subalgebras, ideals, filters, and their respective level sets on Sheffer stroke BE-algebras, demonstrating that the level set of an intuitionistic fuzzy SBE-subalgebra, ideal, or filter is itself a subalgebra, ideal, or filter on this algebra, and vice versa.
Ključne besede: BE-algebra, Sheffer stroke BE-algebra, BE-ideal, intuitionistic fuzzy SBE-subalgebra, intuitionistic fuzzy SBE-ideal
Objavljeno v RUNG: 06.01.2025; Ogledov: 634; Prenosov: 4
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2. Łukasiewicz anti fuzzy subalgebras of BCK/BCI-algebrasJeong Gi Kang, Hashem Bordbar, 2025, izvirni znanstveni članek Opis: 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 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, Υsubset, and anti-subset become subalgebra are explored.
Ključne besede: anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy, subalgebra, Υ-subset, anti subset
Objavljeno v RUNG: 30.10.2024; Ogledov: 917; Prenosov: 1
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3. ŁUKASIEWICZ ANTI FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRASJeong 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: 2334; Prenosov: 0
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4. N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structuresHashem 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: 2917; Prenosov: 44
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6. Internal and external cubic subalgebras of BCK/BCI-algebrasHashem 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: 3297; Prenosov: 0
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8. BMBJ-neutrosophic subalgebra in BCI/BCK-algebrasHashem 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: 4114; Prenosov: 0
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9. Neutrosophic Permeable Values and Energetic Subsets with Applications in BCK/BCI-AlgebrasHashem 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: 4056; Prenosov: 0
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10. Neutrosophic falling shadows applied to subalgebras and ideals in BCK/BCI-algebrasHashem 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: 4063; Prenosov: 0
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