Geodesic
Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals
Bulletin of the Section of Logic, Tome 52 (2023) no. 4, pp. 411-440.

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This paper introduces the concept of single-valued neutrosophic hyper BCK-subalgebras as a generalization and alternative of hyper BCK-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper BCK-subalgebra and one a single-valued neutrosophic hyper BCK-ideal. In this study level subsets play the main role in the connection between singlevalued neutrosophic hyper BCK-subalgebras and hyper BCK-subalgebras and the connection between single-valued neutrosophic hyper BCK-ideals and hyper BCK-ideals. The congruence and (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper BCK-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper BCK-ideals. Indeed, by using the single-valued neutrosophic hyper BCK-ideals, we define a congruence relation on (weak commutative) hyper BCK-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper BCK-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper BCK-subalgebra) BCK-(sub)algebra.
Keywords: single-valued neutrosophic (hyper)\(BCK\)-subalgebra, quasi commutative diagram, extendable single-valued neutrosophic (hyper)\(BCK\)-ideal 
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Hamidi, Mohammad. Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals. Bulletin of the Section of Logic, Tome 52 (2023) no. 4, pp. 411-440. http://geodesic.mathdoc.fr/item/BSL_2023_52_4_a0/

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