1. 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: 520; Downloads: 4
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2. 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: 570; Downloads: 0
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3. 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: 1119; Downloads: 12
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4. 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: 1033; Downloads: 6
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5. 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: 1252; Downloads: 4
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8. 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: 1654; Downloads: 3
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9. 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: 1461; Downloads: 0
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10. Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social SystemsNarjes Firouzkouhi, Reza Ameri, Abbas Amini, Hashem Bordbar, 2022, original scientific article Abstract: Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic
application in some problems. Influenced by these mathematical notions, a novel semihypergroup based graph (SBG) of G = hH, Ei is constructed through the fundamental relation gn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xgny. The connectivity of graph G is characterized by xg y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/g . Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in
the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
Keywords: graph theory, hypergroup, fundamental relation, social systems, geometric space
Published in RUNG: 23.11.2022; Views: 1497; Downloads: 0
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