Katıcan, Tuğçe

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https://hdl.handle.net/20.500.14365/7651
Name Variants
Katican, Tugce
Katican, T.
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tugce.katican@ieu.edu.tr
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02.02. Mathematics
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Current Staff
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0000-0003-1186-6750
Scopus Author ID
57200450829
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WoS Researcher ID
HDN-4339-2022
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28

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207

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19

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19

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24

Scopus Citation Count

22

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1.26

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1.16

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JournalCount
Honam Mathematıcal Journal2
New Mathematics and Natural Computation2
Annali dell'Universita di Ferrara1
Asian-European Journal of Mathematics1
Axioms1
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  • Thumbnail Image
    Article
    Citation - WoS: 4
    Sheffer Stroke Hilbert Algebras Stabilizing by Ideals
    (MDPI, 2024-01-30) Katıcan Tuğçe; Bordbar, Hashem; Katican, Tugce
    This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterwards, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers.
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    Article
    The Characterization of Nelson Algebras by Sheffer Stroke
    (Sciendo, 2025-10-01) Öner, T.; Katican, T.; Borumand Saeid, A.B.; Saeid, Arsham Borumand
    In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras, quotient sets, and fuzzy structures on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. It is also shown that an s-Nelson algebra is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on an s-Nelson algebra is determined by an ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra constructed by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equal to 2. © 2025 Tahsin Oner et al., published by Ovidius University of Constanta.
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    Article
    Citation - Scopus: 1
    Sheffer Stroke R0−Algebras
    (Yazd University, 2023) Katıcan Tuğçe; Öner, T.; Saeid, A.B.; Katican, Tugce
    The main objective of this study is to introduce Sheffer stroke R0−algebra (for short, SR0− algebra). Then it is stated that the axiom system of a Sheffer stroke R0−algebra is independent. It is indicated that every Sheffer stroke R0−algebra is R0−algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R0−algebra are defined, a congruence relation on a Sheffer stroke R0−algebra is determined by the ideal and quotient Sheffer stroke R0−algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R0−algebra constructed by a prime ideal of this algebra is totally ordered and the cardinality is less than or equals to 2. After all, important conclusions are obtained for totally ordered Sheffer stroke R0−algebras by applying various properties of prime ideals. © 2023 Yazd University.
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    Article
    Citation - WoS: 2
    Asymptotic Constancy for Solutions of Abstract Non-Linear Fractional Equations With Delay and Generalized Hilfer ( A, B, A )- Derivatives
    (Pergamon-elsevier Science Ltd, 2025-02) Kostic, Marko; Koyuncuoglu, Halis Can; Katican, Tugce
    In this paper, we investigate the asymptotic constancy for solutions of abstract non-linear fractional differential (difference) equations with delay and generalized Hilfer ( a, b, a )- derivatives. Our results are applicable to the abstract fractional functional equations with the usually considered Riemann-Liouville, Caputo, Hilfer and Prabhakar derivatives.
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    Article
    Hesitant Fuzzy Structures on Sheffer Stroke Bck-Algebras
    (World Scientific Publ Co Pte Ltd, 2022-12-08) 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.
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    Article
    Citation - Scopus: 1
    Characterization of Ideals in L-Algebras by Neutrosophic N- Structures
    (Springer-Verlag Italia s.r.l., 2022-06-14) 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.
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    Article
    Citation - WoS: 2
    Study Strong Sheffer Stroke Non-Associative Mv-Algebras by Fuzzy Filters
    (Ankara Univ, Fac Sci, 2022-03-31) Oner, Tahsin; Katıcan Tuğçe; Borumand Saeid, Arsham; Katican, Tugce; Saeid, Arsham Borumand
    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.
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    Article
    Sheffer Stroke Bl-Algebras Via Intuitionistic Fuzzy Structures
    (World Scientific Publ Co Pte Ltd, 2023-07-07) Öner, Tahsin; Jun, Young Bae; Katıcan Tuğçe; Saeid, Arsham Borumand; Katican, Tugce
    The notions of intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters are defined and examined on Sheffer stroke BL-algebras in detail. Then we characterize the properties of these intuitionistic fuzzy structures, and show the relationships between intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters. Also, it is stated that the affiliations between aforementioned intuitionistic fuzzy structures and ordinary fuzzy structures on Sheffer stroke BL-algebras, and that the upper and lower level sets defining intuitionistic fuzzy (ultra) filters are (ultra) filters on these algebraic structures. At the end of the study, the process of building new intuitionistic fuzzy filters is presented by means of homomorphisms of Sheffer stroke BL-algebras.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 3
    On Ideals of Sheffer Stroke Up-Algebras
    (Taru Publications, 2023) Öner, T.; Katıcan Tuğçe; Katican, Tuğcce
    The goal of the study is to introduce SUP-ideals on Sheffer Stroke UP-algebras (briefly, SUP-algebra) and its properties. We define SUP-ideals of SUP-algebras and then prove some properties. By describing a congruence relation on a SUP-algebra by the SUP-ideal, it is shown that the quotient set defined by the congruence relation is a SUP-algebra. Finally, SUP-homomorphisms on SUP-algebras are determined and the relationships between SUP-ideals of SUP-algebras are examined by means of the SUP-homomorphisms. © 2023, Taru Publications. All rights reserved.
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    Article
    Citation - Scopus: 1
    Neutrosophic N?structures on Sheffer Stroke Bch-Algebras
    (University of New Mexico, 2023-03-30) 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