1. Sheffer stroke Hilbert algebras stabilizing by idealsTugce Katican, Hashem Bordbar, 2024, original scientific article Abstract: This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterward, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers.
Keywords: Hilbert algebra, Sheffer operation, ideal, stabilizer
Published in RUNG: 31.01.2024; Views: 1340; Downloads: 8
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2. Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadowsHashem Bordbar, Xiao Long Xin, Rajab Ali Borzooei, Young Bae Jun, 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.
Keywords: neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Published in RUNG: 06.06.2022; Views: 2285; Downloads: 0
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5. Implicative falling neutrosophic ideals of BCK-algebrasXiao Long Xin, Hashem Bordbar, Florentin Smarandache, Rajab Ali Borzooei, Young Bae Jun, 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.
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 in RUNG: 15.03.2021; Views: 2892; Downloads: 0
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6. UNI-SOFT IDEALS IN CORESIDUATED LATTICESHashem Bordbar, 2018, original scientific article Abstract: The notion of the uni-soft idea is introduced, and related properties are investigated. Characterizations of the uni-soft ideal are discussed. The transfer of uni-soft ideal is considered, and relations between the uni-soft ideal and its transfer are investigated. Given a soft set, conditions for the transfer of soft set to be a uni-soft ideal.
Keywords: Coresiduated lattice, uni-soft ideal, transfer, support.
Published in RUNG: 15.10.2020; Views: 3253; Downloads: 0
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7. Double-framed soft set theory applied to hyper BCK-algebrasHashem Bordbar, 2020, original scientific article Abstract: The notions of double-framed soft hyper BCK-algebra and double-framed soft (strong) hyper BCK-ideal of a hyper BCK-algebra are introduced, and related properties are investigated. Characterizations of double-framed soft hyper BCK-algebra and double- framed soft hyper BCK-ideal are considered. Relations between double-framed soft hyper BCK-ideal and double-framed soft strong hyper BCK-ideal are discussed. Conditions for a double-framed soft set to be a double-framed soft strong hyper BCK-ideal are provided.
Keywords: double-framed soft hyper BCK-algebra, double-framed soft (strong) hyper BCK-ideal.
Published in RUNG: 31.08.2020; Views: 3226; Downloads: 0
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8. 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.
Keywords: Ideal, neutrosophic ∈-subset, neutrosophic qk-subset, neutrosophic ∈∨qk-subset, (∈, ∈ ∨q(kT, kI, kF ))-neutrosophic ideal.
Published in RUNG: 31.08.2020; Views: 3223; Downloads: 0
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