Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Bordbar, Hashem; Jun, Young Bae; Song, Seok-Zun

doi:10.3390/math8040567

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…for all x ∈ X, which shows that • satisfies the condition (13). For every x, y ∈ X, if x ≤ y then (x) ≤ (y), and so ( • )(x) = ( (x)) ≤ ( (y)) = ( • )(y).…”

Section: Example 38mentioning

confidence: 85%

“…For every x ∈ I (X), we havẽ 2 (x) =̃(¬¬ (x)) = ¬¬¬¬ (x) = ¬¬ (x) =̃(x) by (7). Hencẽsatisfies the condition (13). Let x, y ∈ I (X) be such that x ≤ y.…”

Section: Example 38mentioning

confidence: 99%

“…A BCK/BCI-algebra is an important class of logical algebras introduced by K. Iséki (see [5,6]) and was extensively investigated by several researchers. Please refer to [7][8][9][10][11][12][13] We recall the definitions and basic results required in this paper. See the books [14,15] for further information regarding BCK/BCIalgebras.…”

Section: Preliminariesmentioning

confidence: 99%

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Interior BCK/BCI-Algebras

Ahn¹,

Bordbar²,

Jun³

2021

IJCIS

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The notions of interior BCK/BCI-algebras, positive implicative interior BCK-algebras, (weak) interior ideals, positive implicative interior ideals, a positive implicative weak interior ideal of type 1, type 2, and type 3 are introduced, and related properties are investigated. A mapping is provided to the set of all involutions of a bounded BCK-algebra in relation to any interior BCKalgebra so that the set of all involutions of a bounded BCK-algebra can be an interior BCK-algebra. The relationship between interior ideals, weak interior ideals, and positive implicative interior ideals is established. The conditions under which a weak interior ideal can change to an interior ideal are founded. The conditions for an interior ideal to be a positive implicative interior ideal are provided. The scalability for a positive implicative interior ideal is discussed. The relationship between type 1, type 2, and type 3 on positive implicative weak interior ideals are investigated. The relationship between weak interior ideal and positive implicative weak interior ideal of type 1, type 2, and type 3 are established.

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“…for all x ∈ X, which shows that • satisfies the condition (13). For every x, y ∈ X, if x ≤ y then (x) ≤ (y), and so ( • )(x) = ( (x)) ≤ ( (y)) = ( • )(y).…”

Section: Example 38mentioning

confidence: 85%

“…For every x ∈ I (X), we havẽ 2 (x) =̃(¬¬ (x)) = ¬¬¬¬ (x) = ¬¬ (x) =̃(x) by (7). Hencẽsatisfies the condition (13). Let x, y ∈ I (X) be such that x ≤ y.…”

Section: Example 38mentioning

confidence: 99%

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Interior BCK/BCI-Algebras

Ahn¹,

Bordbar²,

Jun³

2021

IJCIS

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“…Although the literature consists of several studies on BCKalgebras, importance seems to have been particularly attach to the ideal theory of BCKalgebras. For more details, recent studies [2][3][4][5][6][7][8][9][10] can be suggested in literature.…”

Section: Introductionmentioning

confidence: 99%

BCK-cebirlerinin Sheffer stroke dallanması

KATİCAN

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The main objective of the study is to introduce branches of Sheffer stroke BCK-algebras due their specific elements. At the onset of the study, an atom of a Sheffer stroke BCK-algebra is defined and it is shown that the set of all atoms of the algebraic structure is its subalgebra. Then it is proved that specified subsets defined by atoms of a Sheffer stroke BCK-algebra are ideals but the inverses are not true in general. Moreover, a branch and a chain on a Sheffer stroke BCK-algebra are introduced and some properties are presented. Finally, relationships between aforementioned concepts are built and supported by illustrative examples.

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“…Jun et al [14], [2], [3] have discussed soft set theory in residuated lattices. Jun and Park [17], Bordbar [1], [4], [5], [6], [7] and [8] studied applications of soft sets in ideal theory of BCK/BCI-algebras. Jun et al [15,16] introduced the notion of intersectional soft sets, and considered its applications to BCK/BCI-algebras.…”

Section: Introductionmentioning

confidence: 99%