1. 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: 234; Downloads: 2
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5. 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: 588; Downloads: 0
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6. 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: 696; Downloads: 0
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7. Regular local hyperrings and hyperdomainsHashem Bordbar, Irina Cristea, Sanja Rasovic, 2022, original scientific article Abstract: This paper falls in the area of hypercompositional algebra. In particular, it focuses on the
class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R.
Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Published in RUNG: 27.09.2022; Views: 807; Downloads: 19
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8. 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: 1068; Downloads: 0
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10. The Structure of the Block Code Generated by a BL-AlgebraHashem Bordbar, 2022, original scientific article Abstract: Inspired by the concept of BL-algebra as an important part of the ordered algebra, in this paper we investigate the binary block code generated by an arbitrary BL-algebra and study related properties. For this goal, we initiate the study of the BL-function on a nonempty set P based on BL-algebra L, and by using that, l-functions and l-subsets are introduced for the arbitrary element l of a BL-algebra. In addition, by the mean of the l-functions and l-subsets, an equivalence relation on the BL-algebra L is introduced, and using that, the structure of the code generated by an arbitrary BL-algebra is considered. Some related properties (such as the length and the linearity) of the generated code and examples are provided. Moreover, as the main result, we define a new order on the generated code C based on the BL-algebra L, and show that the structures of the BL-algebra with its order and the correspondence generated code with the defined order are the same.
Keywords: BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Published in RUNG: 07.03.2022; Views: 1189; Downloads: 38
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