Browsing by Author "Oner, Tahsin"

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Citation - WoS: 8
BL-ALGEBRAS DEFINED BY AN OPERATOR
(Honam Mathematical Soc, 2022) Oner, Tahsin; Katıcan Tuğçe; Saeid, Arsham Borumand
In this paper, Sheffer stroke BL-algebra and its properties are investigated. It is shown that a Cartesian product of two Sheffer stroke BL-algebras is a Sheffer stroke BL-algebra. After describing a filter of Sheffer stroke BL-algebra, a congruence relation on a Sheffer stroke BL-algebra is defined via its filter, and quotient of a Sheffer stroke BL-algebra is constructed via a congruence relation. Also, it is defined a homomorphism between Sheffer stroke BL-algebras and is presented its properties. Thus, it is stated that the class of Sheffer stroke BL-algebras forms a variety.
Citation - Scopus: 1
Characterization of Ideals in L-Algebras by Neutrosophic N- Structures
(Springer-Verlag Italia s.r.l., 2023) Katıcan Tuğçe; Oner T.; Borumand Saeid A.; Katican, Tugce; Oner, Tahsin; Borumand Saeid, Arsham
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.
Citation - Scopus: 2
Fuzzy Ideals of Sheffer Stroke Hilbert Algebras
(Springer, 2023) Oner T.; Katıcan Tuğçe; Borumand Saeid A.; Katican, Tugce; Oner, Tahsin; Borumand Saeid, Arsham
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.
Hesitant Fuzzy Structures on Sheffer Stroke Bck-Algebras
(World Scientific Publ Co Pte Ltd, 2022) Oner, Tahsin; Katıcan Tuğçe; Saeid, Arsham Borumand; Katican, Tugce
The main objective of the study is to introduce a hesitant fuzzy structures on Sheffer stroke BCK-algebras related to their subsets (subalgebras as possible as). Then it is proved that every hesitant fuzzy ideal of a Sheffer stroke BCK-algebra related to the subset is the hesitant fuzzy subalgebra. By defining a hesitant fuzzy maximal ideal in this algebra, relationships between aforementioned structures, subalgebras and ideals on Sheffer stroke BCK-algebras are shown in detail. Finally, it is illustrated that a subset of a Sheffer stroke BCK-algebra defined by a certain element and a hesitant fuzzy (maximal) ideal on the algebra is a (maximal) ideal but the inverse is usually not true.
Citation - Scopus: 1
Neutrosophic N?structures on Sheffer Stroke Bch-Algebras
(University of New Mexico, 2022) Oner T.; Katıcan Tuğçe; Rezaei A.; Katican, Tugce; Rezaei, Akbar; Oner, Tahsin
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
Citation - WoS: 1
STABILIZERS ON SHEFFER STROKE BL-ALGEBRAS
(Honam Mathematical Soc, 2022) Katıcan Tuğçe; Oner, Tahsin; Saeid, Arsham Borumand
In this study, new properties of various filters on a Sheffer stroke BL-algebra are studied. Then some new results in filters of Sheffer stroke BL-algebras are given. Also, stabilizers of nonempty subsets of Sheffer stroke BL-algebras are defined and some properties are examined. Moreover, it is shown that the stabilizer of a filter with respect to a/n (ultra) filter of a Sheffer stroke BL-algebra is its (ultra) filter. It is proved that the stabilizer of the subset {0} of a Sheffer stroke BL-algebra is {1}. Finally, it is stated that the stabilizer St(P, Q) of P with respect to Q is an ultra filter of a Sheffer stroke BL-algebra when P is any filter and Q is an ultra filter of this algebra.
Study Groupoids by Sheffer Stroke
(World Scientific Publ Co Pte Ltd, 2025) Katican, Tugce; Oner, Tahsin; Hamal, Ahmet; Saeid, Arsham Borumand
In this study, we study groupoids by Sheffer stroke. By defining subgroupoids and ideals of a groupoid with Sheffer stroke, it is proved that every ideal of a groupoid with Sheffer stroke is a subgroupoid but the converse is generally not true. Also, a congruence relation is described on the groupoid by means of ideals, and a quotient groupoid with Sheffer stroke is constructed via this congruence. Finally, relationships between Sheffer stroke algebras and this groupoid are presented.
Citation - WoS: 2
Study Strong Sheffer Stroke Non-Associative Mv-Algebras by Fuzzy Filters
(Ankara Univ, Fac Sci, 2022) Oner, Tahsin; Katıcan Tuğçe; Borumand Saeid, Arsham
In this paper, some types of fuzzy filters of a strong Sheffer stroke non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are introduced. By presenting new properties of filters, we define a prime filter in this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke NMV-algebra are determined and some features are proved. Finally, we built quotient strong Sheffer stroke NMV-algebra by a fuzzy filter.