Browsing by Author "Saeid, Arsham Borumand"

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Another View of BZ-Algebras
(University of Guilan, 2025) Öner, T.; Katican, T.; Borumand Saeid, A.B.; Saeid, Arsham Borumand
In this work, Sheffer stroke BZ-algebra (briefly, SBZ-algebra) is introduced and its properties are examined. Then a partial order is defined on SBZ-algebras. It is shown that a Cartesian product of two SBZ-algebras is an SBZ-algebra. After giving SBZ-ideals and SBZ-subalgebras, it is proved that any SBZ-ideal of an SBZ-algebra is an ideal of this SBZ-algebra and vice versa, and that it is also an SBZ-subalgebra. Also, a congruence relation on an SBZ-algebra is determined by an SBZ-ideal, and the quotient of an SBZ-algebra by a congruence relation on this algebra is constructed. Thus, it is proved that the quotient of the SBZ-algebra is an SBZ-algebra. Furthermore, we define SBZ-homomorphisms between SBZ-algebras and state that the kernel of an SBZ-homomorphism is an SBZ-ideal and so an SBZ-subalgebra. Hence, a new SBZ-homomorphism is described by means of the kernel of an SBZ-homomorphism. Finally, we show that some properties are preserved under SBZ-homomorphisms. © 2025 University of Guilan.
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.
The Characterization of Nelson Algebras by Sheffer Stroke
(Sciendo, 2025) 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.
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.
Sheffer Stroke Bl-Algebras Via Intuitionistic Fuzzy Structures
(World Scientific Publ Co Pte Ltd, 2023) 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.
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.