Katıcan, Tuğçe
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Katican, Tugce
Katican, T.
Katican, T.
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tugce.katican@ieu.edu.tr
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02.02. Mathematics
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Sustainable Development Goals
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28
Citations
207
h-index
9
Documents
23
Citations
143
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18
Articles
18
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2/0
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0
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0
WoS Citation Count
24
Scopus Citation Count
22
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3
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3
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0
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0
WoS Citations per Publication
1.33
Scopus Citations per Publication
1.22
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5
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18 results
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Now showing 1 - 10 of 18
Article Citation - WoS: 4Sheffer Stroke Hilbert Algebras Stabilizing by Ideals(MDPI, 2024) Katıcan Tuğçe; Bordbar, HashemThis 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.Article Citation - Scopus: 1Sheffer Stroke R0−Algebras(Yazd University, 2023) Katıcan Tuğçe; Öner, T.; Saeid, A.B.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.Article The Characterization of Nelson Algebras by Sheffer Stroke(Sciendo, 2025) Öner, T.; Katican, T.; Borumand Saeid, A.B.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.Article Citation - WoS: 2Asymptotic Constancy for Solutions of Abstract Non-Linear Fractional Equations With Delay and Generalized Hilfer ( A, B, A )- Derivatives(Pergamon-elsevier Science Ltd, 2025) Kostic, Marko; Koyuncuoglu, Halis Can; Katican, TugceIn 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.Article Citation - WoS: 1Citation - Scopus: 3On Ideals of Sheffer Stroke Up-Algebras(Taru Publications, 2023) Öner, T.; Katıcan TuğçeThe 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.Article Sheffer Stroke Bl-Algebras Via Intuitionistic Fuzzy Structures(World Scientific Publ Co Pte Ltd, 2023) Öner, Tahsin; Jun, Young Bae; Katıcan Tuğçe; Saeid, Arsham BorumandThe 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.Article Neutrosophic N−ideals on Sheffer Stroke Bck-Algebras(The Indonesian Mathematical Society, 2023) Öner, T.; Katican T.; Rezaei, A.In this study, a neutrosophic N−subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N−subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals. © 2023 The Author(s).Article Hesitant Fuzzy Structures on Sheffer Stroke Bck-Algebras(World Scientific Publ Co Pte Ltd, 2022) Oner, Tahsin; Katıcan Tuğçe; Saeid, Arsham BorumandThe 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.Article Citation - WoS: 2Study Strong Sheffer Stroke Non-Associative Mv-Algebras by Fuzzy Filters(Ankara Univ, Fac Sci, 2022) Oner, Tahsin; Katıcan Tuğçe; Borumand Saeid, ArshamIn 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.Article Citation - WoS: 3Citation - Scopus: 11On Sheffer Stroke Be-Algebras(Sciendo, 2022) Katican, T.; Oner, T.; Saeid, A.B.In this paper we introduce Sheffer stroke BE-Algebras (briefly, SBE-Algebras) and investigate a relationship between SBE-Algebras and BE-Algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-Algebra, it is shown that any SBE-filter of a SBE-Algebra is a SBE-subalgebra but the converse of this statement is not true. Besides we construct quotient SBE-Algebras via a congruence relation defined by a special SBE-filter. We discuss SBE-homomorphisms and their properties between SBE-Algebras. Finally, a relation between Sheffer stroke Hilbert algebras and SBE-Algebras is established. © 2022 Tugce Katican et al., published by Sciendo.
