1. Łukasiewicz anti fuzzy subalgebras of BCK/BCI-algebrasJeong Gi Kang, Hashem Bordbar, 2025, original scientific article 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 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. Keywords: anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy, subalgebra, Υ-subset, anti subset Published in RUNG: 30.10.2024; Views: 232; Downloads: 0 Full text (406,85 KB) |
2. A characterization of normal injective and normal projective hypermodulesErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: This study is motivated by the recently published papers on normal injective and normal
projective hypermodules. We provide a new characterization of the normal injective and normal
projective hypermodules by using the splitting of the short exact sequences of hypermodules. After presenting some of their fundamental properties, we show that if a hypermodule is normal projective, then every exact sequence ending with it is splitting. Moreover, if a hypermodule is a normal injective, then every exact sequence starting with it is splitting as well. Finally, we investigate the relationships between semisimple, simple, normal injective, and normal projective hypermodules. Keywords: short exact sequence, normal injective hypermodule, normal projective hypermodule Published in RUNG: 20.06.2024; Views: 735; Downloads: 6 Full text (277,55 KB) This document has many files! More... |
3. Categorical approach of normal injective and torsionable hypermodulesHashem Bordbar, 2024, published scientific conference contribution abstract Abstract: Inspired by the characterization of injective objects in category theory,
our main purpose in this research is to investigate the relationships of di-
visible and injective hypermodules with torsion elements and torsionable
hypermodules with a category approach. These days, it is extremely
tempt- ing to do the research in an Abelian category, so we discuss these
topics in an Abelian category. For a Krasner R-hypermodule M, we ex-
tend the definition of a zero-divisor element of R to a zero-divisor ele-
ment of R over M, and then the definition of divisible R-hypermodule is
introduced. Be- sides, the torsion element and torsionable hypermodule
are introduced and we show that every torsionable R-hypermodule M is a
normal injective, where R is a commutative hyperring. Keywords: hypermodules, hyperrings, normal injective, normal projective Published in RUNG: 18.06.2024; Views: 777; Downloads: 0 This document has many files! More... |
4. A hyperstructural approach to semisimplicityErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article Abstract: In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M), ·) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hypermodule is normal projective with a zero singular subhypermodule. We also show that the class of semisimple hypermodules is closed under internal direct sums, factor hypermodules, and subhypermodules. In particular, we give a characterization of internal direct sums of subhypermodules of a hypermodule. Keywords: direct sum, simple hypermodule, semisimple hypermodule Published in RUNG: 31.01.2024; Views: 1406; Downloads: 14 Full text (328,98 KB) This document has many files! More... |
5. 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: 1245; Downloads: 8 Full text (320,63 KB) This document has many files! More... |
6. Torsion elements and torsionable hypermodulesHashem Bordbar, 2023, original scientific article Abstract: This article is motivated by the recently published studies on divisible hypermodules and
falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it, we introduce a new class of hypermodules, namely the torsionable hypermodule. After investigating some of their fundamental properties, we will show that the class of torsionable hypermodules is a subclass of the class of divisible hypermodules. Finally, we present the relationships between divisible, torsionable, and normal injective hypermodules. Keywords: hypermodules, zero divisors, torsion elements, torsionable hypermodules, normal injective hypermodules Published in RUNG: 03.11.2023; Views: 1528; Downloads: 4 Full text (274,24 KB) This document has many files! More... |
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9. Advanced artificial intelligence system by intuitionistic fuzzy ▫$\Gamma$▫ -subring for automotive robotic manufacturingNarjes Firouzkouhi, Abbas Amini, Marziyeh Nazari, Fadi Alkhatib, Hashem Bordbar, Chun Cheng, Bijan Davvaz, Maria Rashidi, 2023, original scientific article Keywords: intelligent systems, robotic manufacturing, intuitionistic fuzzy set, image, inverse image, upper bound level, lower bound level Published in RUNG: 03.03.2023; Views: 1851; Downloads: 3 Link to file This document has many files! More... |
10. ŁUKASIEWICZ ANTI FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRASJeong Gi Kang, Hashem Bordbar, 2025, original scientific article Abstract: 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. Keywords: Anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy subalgebra, ⋖-subset, Υ-subset, anti subset Published in RUNG: 20.02.2023; Views: 1651; Downloads: 0 This document has many files! More... |