11. Regular local hyperrings and hyperdomainsHashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, izvirni znanstveni članek Opis: 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.
Ključne besede: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Objavljeno v RUNG: 27.09.2022; Ogledov: 1240; Prenosov: 21
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12. Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadowsHashem Bordbar, Xiao Long Xin, Rajab Ali Borzooei, Young Bae Jun, 2022, izvirni znanstveni članek Opis: 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.
Ključne besede: neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Objavljeno v RUNG: 06.06.2022; Ogledov: 1632; Prenosov: 0
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14. The Structure of the Block Code Generated by a BL-AlgebraHashem Bordbar, 2022, izvirni znanstveni članek Opis: 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.
Ključne besede: BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Objavljeno v RUNG: 07.03.2022; Ogledov: 1675; Prenosov: 47
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16. BCK codesHashem Bordbar, 2022, izvirni znanstveni članek Opis: In this paper, we initiate the study of the notion of the BC K -function on an arbitrary set A, and providing connections with x -functions and x -subsets for x ∈ X where X is a B C K -algebra. Moreover, using the notion of order in a B C K -algebra, the BCK-code C is introduced and besides a new structure of order in C is investigated. Finally, we show that the structure of the B C K -algebra X and the B C K -code C which is generated by X , with their related orders are the same.
Ključne besede: BCK -function, x-functions, x-subsets, BCK -codes, binary linear block codes
Objavljeno v RUNG: 04.01.2022; Ogledov: 1653; Prenosov: 8
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17. N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structuresHashem Bordbar, Mohammad Rahim Bordbar, Rajab Ali Borzooei, Young Bae Jun, 2021, izvirni znanstveni članek Opis: In the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets
and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37],
Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization
of fuzzy sets and interval-valued fuzzy sets and applied it to
group theory. The aim of this manuscript is to study N-structures in
BCK\BCI-algebras induced from hyperfuzzy structures.
Ključne besede: hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N-function
Objavljeno v RUNG: 03.11.2021; Ogledov: 1821; Prenosov: 42
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19. Codes generated by ordered algebraic structuresHashem Bordbar, 2021, objavljeni povzetek znanstvenega prispevka na konferenci Opis: Error-control codes are used to detect and correct errors that occur when data are trans-mitted across some noisy channel or stored on some medium. The study of error-control codes is called coding theory and emerged in 1948 by Claud Shannon's paper which demonstrated that by proper encoding of the data, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transmission. Some algebraic structures, includes the study and discovery of various coding schemes, are used to increase the number of errors that can be corrected during data transmission. One of the classes of logical algebra is ordered algebras which were introduced by Imai and Iseki in 1966. In this note, I study the codes generating by the ordered algebraic structures such as BCK-algebras and BL-algebras. For this goal, symmetric rela-tions on these ordered structures facilitate us to design the correspondence codeword. Moreover, I show that the structure of ordered algebra and the code generated by it will be the same.
Ključne besede: coding theory, BCK-algebra, BL-algebra
Objavljeno v RUNG: 20.08.2021; Ogledov: 2141; Prenosov: 150
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20. Interior BCK/BCI-algebrasSun Shin Ahn, Hashem Bordbar, Young Bae Jun, 2021, izvirni znanstveni članek Opis: 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.
Ključne besede: interior BCK/BCI-algebras, positive implicative interior, BCK-algebras, (weak) interior ideals, positive implicative interior ideals
Objavljeno v RUNG: 21.07.2021; Ogledov: 2029; Prenosov: 45
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