Browsing by Author "Oner T."

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    Characterization of Ideals in L-Algebras by Neutrosophic N- Structures
    (Springer-Verlag Italia s.r.l., 2023) Katıcan Tuğçe; Oner T.; Borumand Saeid A.
    The main objective of this study is to introduce a neutrosophic N- subalgebra (ideal) of L-algebras and to investigate some properties. It is shown that the level-set of a neutrosophic N- subalgebra (ideal) of an L-algebra is its subalgebra (ideal), and the family of all neutrosophic N- subalgebras of an L-algebra forms a complete distributive modular lattice. Additionally, it is proved that every neutrosophic N- ideal of an L-algebra is the neutrosophic N- subalgebra but the inverse of the statement may not be true in general. As the concluding part, some special cases are provided as ideals which are particular subsets of an L-algebra defined due to N- functions. © 2022, The Author(s) under exclusive license to Università degli Studi di Ferrara.
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    Fuzzy Ideals of Sheffer Stroke Hilbert Algebras
    (Springer, 2023) Oner T.; Katıcan Tuğçe; Borumand Saeid A.
    In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T (briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and T-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm T (in short, T-fuzzy ideal) is a T-fuzzy subalgebra but the converse does not generally hold. As in T-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the T-fuzzy ideals are proved. © 2022, The Author(s), under exclusive licence to The National Academy of Sciences, India.
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    Neutrosophic N?structures on Sheffer Stroke Bch-Algebras
    (University of New Mexico, 2022) Oner T.; Katıcan Tuğçe; Rezaei A.
    The aim of the study is to introduce a neutrosophic N?subalgebra and neutrosophic N?ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N?subalgebra (neutrosophic N?ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N?subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N?ideal of a Sheffer stroke BCH-algebra is its neutrosophic N?subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N?ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N?functions on this algebraic structure and some properties are investigated. © 2022