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52. N-subalgebras of BCK=BCI-algebras which are induced from hyperfuzzy structuresYoung Bae Jun, Rajab Ali Borzooei, Hashem Bordbar, Mohammad Rahim Bordbar, 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.
Najdeno v: osebi
Ključne besede: hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N-function
Objavljeno: 03.11.2021; Ogledov: 849; Prenosov: 34
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53. 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.
Najdeno v: osebi
Ključne besede: BCK -function, x-functions, x-subsets, BCK -codes, binary linear block codes
Objavljeno: 04.01.2022; Ogledov: 772; Prenosov: 5
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55. Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadowsYoung Bae Jun, Rajab Ali Borzooei, Xiao Long Xin, Hashem Bordbar, 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.
Najdeno v: osebi
Ključne besede: neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Objavljeno: 06.06.2022; Ogledov: 563; Prenosov: 0
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