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Öğe An Algebraic Analysis of Categorical Syllogisms by Using Carroll's Diagrams(Univ Nis, Fac Sci Math, 2019) Senturk, Ibrahim; Oner, TahsinDaha fazla In this paper, we analyze the algebraic properties of categorical syllogisms by constructing a logical calculus system called Syllogistic Logic with Carroll Diagrams (SLCD). We prove that any categorical syllogism is valid if and only if it is provable in this system. For this purpose, we explain firstly the quantitative relation between two terms by means of bilateral diagrams and we clarify premises via bilateral diagrams. Afterwards, we input the data taken from bilateral diagrams, on the trilateral diagram. With the help of the elimination method, we obtain a conclusion that is transformed from trilateral diagram to bilateral diagram. Subsequently, we study a syllogistic conclusion mapping which gives us a conclusion obtained from premises. Finally, we allege valid forms of syllogisms using algebraic methods, and we examine their algebraic properties, and also by using syllogisms, we construct algebraic structures, such as lattices, Boolean algebras, Boolean rings, and many-valued algebras (MV-algebras).Daha fazla Öğe An alternative construction of graphs by associating with algorithmic approach on MV-algebras(Springer, 2021) Gursoy, Arif; Gursoy, Necla Kircali; Oner, Tahsin; Senturk, IbrahimDaha fazla In this paper, we introduce an alternative construction of graphs on MV-algebras. We called them as MV-graphs whose vertices are the elements of MV-algebra and whose edges are the association of two vertices. We also define graphs of equivalence classes by constructing (Delta) over bar -connection operator and complement annihilator on MV-algebras. We prove some related results based on the algebraic properties of graphs. We handle formation of graph folding on MV-algebras. And, we prove the relation between graphs folding and equivalence classes graph of MV-algebras. Moreover, we associate all of these processes with algorithms to serve related areas that used effectively MV-algebras.Daha fazla Öğe BL-ALGEBRAS DEFINED BY AN OPERATOR(Honam Mathematical Soc, 2022) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla 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.Daha fazla Öğe Class of Sheffer stroke BCK-algebras(Ovidius Univ Press, 2022) Oner, Tahsin; Kalkan, Tugce; Saeid, Arsham BorumandDaha fazla In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.Daha fazla Öğe Congruences of Sheffer stroke basic algebras(Ovidius Univ Press, 2020) Senturk, Ibrahim; Oner, Tahsin; Borumand Saeid, ArshamDaha fazla In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. in addition to these, a basic algebra is constructed by the help of compatible filter and A/Theta(F). Moreover, a representation theorem for Sheffer stroke basic algebra by using prime filters and A/Theta(F) is stated and proved.Daha fazla Öğe Filters of strong Sheffer stroke non-associative MV-algebras(Ovidius Univ Press, 2021) Oner, Tahsin; Katican, Tugce; Saeid, Arsham Borumand; Terziler, MehmetDaha fazla In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.Daha fazla Öğe Fuzzy filters of Sheffer stroke Hilbert algebras(Ios Press, 2021) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.Daha fazla Öğe Fuzzy Ideals of Sheffer Stroke Hilbert Algebras(Natl Acad Sciences India, 2022) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla 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.Daha fazla Öğe FUZZY IMPLICATIVE IDEALS OF SHEFFER STROKE BG-ALGEBRAS(Univ Nis, 2021) Oner, Tahsin; Kalkan, Tugce; Katican, Tugce; Rezaei, AkbarDaha fazla In this paper, an (implicative) ideal and a fuzzy ideal of Sheffer stroke BG-algebra are defined and some properties are presented. Then a fuzzy implicative and a sub-implicative ideals of a Sheffer stroke BG-algebra are described. Morever, an implicative Sheffer stroke BG-algebra and a medial Sheffer stroke BG-algebra are defined, and it is expressed that every medial Sheffer stroke BG-algebra is an implicative Sheffer stroke BG-algebra. Also, a fuzzy (completely) closed ideal and a fuzzy p-ideal are determined. Finally, the relationships between these structures are shown.Daha fazla Öğe (FUZZY) FILTERS OF SHEFFER STROKE BL-ALGEBRAS(Univ Kragujevac, Fac Science, 2023) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla In this study, some (fuzzy) filters of a Sheffer stroke BL-algebra and its properties are presented. To show a relationship between a filter and a fuzzy filter of Sheffer stroke BL-algebra, we prove that f is a fuzzy (ultra) filter of C if and only if fp is either empty or a (ultra) filter of C for each p is an element of [0, 1], and it is satisfied for p = f (1) and for the characteristic function of a nonempty subset of a Sheffer stroke BL-algebra.Daha fazla Öğe Hesitant Fuzzy Structures on Sheffer Stroke BCK-Algebras(World Scientific Publ Co Pte Ltd, 2022) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla 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.Daha fazla Öğe (Hesitant) Fuzzy sets on Sheffer stroke UP-algebras(Taylor & Francis Ltd, 2022) Oner, Tahsin; Katican, Tugce; Saeid, Arsham BorumandDaha fazla The aim of this study is to present (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets on Sheffer stroke UP-algebra (in short, SUP-algebra). After defining (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets of a SUP-algebra, we give their some properties and analyse whether the intersection or union of these subalgebras is a (sup-hesitant) fuzzy SUP-subalgebra of a SUP-algebra. It is shown that the level sets of (sup-hesitant) fuzzy SUP-subalgebras of a SUP-algebra are its SUP-subalgebras. Also, fuzzy duplex SUP-sets of a SUP-algebra are determined and studied the cases which these sets are SUP-algebras. Finally, the relationships between aforementioned structures are investigated.Daha fazla Öğe IDEALS OF SHEFFER STROKE HILBERT ALGEBRAS BASED ON FUZZY POINTS(Honam Mathematical Soc, 2024) Jun, Young bae; Oner, TahsinDaha fazla The main objective of the study is to introduce ideals of Sheffer stroke Hilbert algebras by means of fuzzy points, and investigate some properties. The process of making (fuzzy) ideals and fuzzy deductive systems through the fuzzy points of Sheffer stroke Hilbert algebras is illustrated, and the (fuzzy) ideals and the fuzzy deductive systems are characterized. Certain sets are defined by virtue of a fuzzy set, and the conditions under which these sets can be ideals are revealed. The union and intersection of two fuzzy ideals are analyzed, and the relationships between aforementioned structures of Sheffer stroke Hilbert algebras are built.Daha fazla Öğe INDEPENDENCE OF COUNTABLE SETS OF FORMULAS OF THE PROPOSITIONAL LOGIC(Charles Babbage Res Ctr, 2013) Oner, Tahsin; Terziler, MehmetDaha fazla In this paper, we prove that every countable set of formulas of the propositional logic has at least one equivalent independent subset. We illustrate the situation by considering axioms for Boolean algebras; the proof of independence we give uses model forming.Daha fazla Öğe An Independent Set of Axioms of MV-Algebras and Solutions of the Set-Theoretical Yang-Baxter Equation(Mdpi Ag, 2017) Oner, Tahsin; Senturk, Ibrahim; Oner, GulsahDaha fazla The aim of this paper is to give a new equivalent set of axioms for MV-algebras, and to show that the axioms are independent. In addition to this, we handle Yang-Baxter equation problem. In conclusion, we construct a new set-theoretical solution for the Yang-Baxter equation by using MV-algebras.Daha fazla Öğe INFINITE SYMMETRIC GROUPS(Charles Babbage Res Ctr, 2012) Oner, TahsinDaha fazla In this work, infinite similarities of permutation groups are investigated by means of new methods. For this purpose, we handle distinct groups on the set of natural numbers and we give the separation of the subgroups of them. Afterwards, we give the matrix representation of this groups.Daha fazla Öğe An interpretation on Sheffer stroke reduction of some algebraic structures(Amer Inst Physics, 2019) Senturk, Ibrahim; Oner, TahsinDaha fazla In this paper, we obtain Sheffer stroke reduction for some algebraic structures such as BCK-algebras, MV-algebras, Wajsberg algebras and etc. by means of representing all operators in these structures with only Sheffer stroke basic algebras. We also examine some equalities and inequalities which are used in these constructions. in addition, we examine whether there is a transition from one of these structures to another by the help of this reduction.Daha fazla Öğe Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation(Walter De Gruyter Gmbh, 2021) Oner, Tahsin; Katican, TugceDaha fazla In this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features.Daha fazla Öğe NEUTROSOPHIC N-IDEALS ON SHEFFER STROKE BCK-ALGEBRAS(Indonesian Mathematical Soc, 2023) Oner, Tahsin; Katican, Tugce; Rezaei, AkbarDaha fazla 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.Daha fazla Öğe Neutrosophic N-Structures Applied to Sheffer Stroke BL-Algebras(Tech Science Press, 2021) Katican, Tugce; Oner, Tahsin; Rezaei, Akbar; Smarandache, FlorentinDaha fazla In this paper, we introduce a neutrosophic Arsubalgebra, a (ultra) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties on a Sheffer stroke BL-algebra. By defining a quasi-subalgebra of a Sheffer stroke BL-algebra, it is proved that the level set of neutrosophic N-subalgebras on the algebraic structure is its quasi-subalgebra and vice versa. Then we show that the family of all neutrosophic N-subalgebras of a Sheffer stroke BL-algebra forms a complete distributive lattice. After that a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is described, we demonstrate that every neutrosophic N-filter of a Sheffer stroke BL-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. Finally, it is presented that a level set of a (ultra) neutrosophic N-filter of a Sheffer stroke BL-algebra is also its (ultra) filter and the inverse is always true, Moreover, some features of neutrosophic N-structures on a Sheffer stroke BL-algebra are investigated.Daha fazla