Papers by akın osman atagün
A New Soft Set Operation: Complementary Soft Binary Piecewise Intersection (∩) Operation
Black Sea Journal of Engineering and Science
The soft set theory developed by Molodtsov has been applied both theoretically and practically in... more The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and used since its introduction. In this paper, we define a new soft set operation, called complementary soft binary piecewise intersection operation, a unique soft set operation, and examine its basic algebraic properties. Additionally, we aim to contribute to the literature on soft sets by illuminating the relationships between this new soft set operation and other kinds of soft set operations by researching the distribution of this new soft set operation over other soft set operations. Moreover, we prove that the set of all the soft sets with a fixed parameter set together with the complementary soft binary piecewise intersection operation and the soft binary piecewise union operation is a zero-symmetric near-semiring and hemiring.
Soft set theory was firstly introduced by Molodtsov [1].In the papers[1,2,3], the soft set theory... more Soft set theory was firstly introduced by Molodtsov [1].In the papers[1,2,3], the soft set theory was succesfully applied in several directions, such as smoothness of functions, gametheory, operations research, riemann integration, Perron integration, probability, theory of measurement and so on.Gong et al.[4] presented bijective soft set theory. Since it is easy to store and manipulate matrices, transferring of bijective soft sets to soft matrices is very useful. Soft matrices which are representations of soft sets was firstly defined by Çağman and Enginoğlu[5]. In this study, we construct bijective soft matrix theory and investigate some properties of bijective soft matrices, in detail. We demonstrate some matrix operations are preserved for bijective soft matrices, such as AND product.Finally, we indicate that can use the bijective soft matrices in decision making problems.
Strait soft sets and strait rough sets with applications in decision making
Soft Computing
Strait fuzzy sets, strait fuzzy rough sets and their similarity measures-based decision making systems
International Journal of Systems Science
The concept or a group is of rundan1cntal itnportance in the study of algebra. Crroups which arc,... more The concept or a group is of rundan1cntal itnportance in the study of algebra. Crroups which arc, f1·on1 the point of view of algebraic structure. c~~cntially the san1e are said to be ison1orphic. The ideal ain1 of finite group theory is to find all linitc group : that i ~. to '>hO\\ ho\\' to construct finite groups or every possible type. and to establish effective procedures '' h ich wi 11 detcnn i ne \\het her t \\O given fin itc groups are of the san1e type. W c added a ne\v one on all present techniques: Group Matricc". This technique is easier and shorter than the all present techniques to obtain all finite groups of the san1c finite order. Since this technique includes n1atrices, the theory can be translated to cornputational progratntning in the ruturc.
N-group SI-action and its application to N-group theory
A new view on vector spaces: Soft vector spaces
Southeast Asian Bulletin of Mathematics
Molodtsov introduced the concept of soft sets. In this paper, we present the de�finition of soft ... more Molodtsov introduced the concept of soft sets. In this paper, we present the de�finition of soft vector spaces and construct some basic properties by using vector spaces and Molodtsov's de�finition of soft sets. We introduce the notions of soft vector spaces, soft subvector spaces, soft v-linear transformations and soft b-linear transforma tions and some related properties of soft structures over vector spaces are investigated and illustrated by many examples. Also soft v-linear transformation are investigated with respect to the soft linear transformatic image and we show that some structures of soft vector spaces are preserved under soft b-linear transformations.
Uni-soft substructures of groups
ABSTRACT In this paper, we introduce the notion of uni-soft subgroups and uni-soft normal subgrou... more ABSTRACT In this paper, we introduce the notion of uni-soft subgroups and uni-soft normal subgroups of a group by us ing the definition of soft sets and investigate their related properties especially with respect to anti image, alpha-inclusions of soft sets and group homomorphism. We also obtain some significant relations between int-soft subgroups and uni-soft subgroups.
Soft Intersection Interior Ideals, Quasi-ideals and Generalized Bi-Ideals; A New Approach to Semigroup Theory II
Filomat, 2015
In this paper, we define soft intersection semigroups, soft intersection left (right, two-sided) ... more In this paper, we define soft intersection semigroups, soft intersection left (right, two-sided) ideals and bi-ideals of semigroups, give their properties and interrelations and we characterize regular, intra-regular, completely regular, weakly regular and quasi-regular semigroups in terms of these ideals.
Yak n-halkalarda asalln bir cok farkl genelle tirilmesi callm t r. Bu cal mada, asal yak nhalkala... more Yak n-halkalarda asalln bir cok farkl genelle tirilmesi callm t r. Bu cal mada, asal yak nhalkalar icin c1-asal yak n-halkalar ad yla yeni bir genelle tirme verilmi tir. Bir N yak n-halkas uzerinde, c1N-grup kavram tan mlanm ve c1-asal yak n-halkalar ile c1-N-gruplar aras nda literature uygun bir ili ki oldu u ispatlanm t r. 1990 y l nda Booth, Groenewald ve Veldsman taraf ndan tan t lan e-asal yak nhalkalar n, ayn zamanda c1-asal oldu u ispatlanm t r. Bunun tersinin yak n-halkan n s f r-simetrik olmas halinde bile do ru olmayaca na bir ornek verilmi tir
Scientia Iranica, 2021
The decompositions of soft sets and soft matrices are important tools for theoretical and practic... more The decompositions of soft sets and soft matrices are important tools for theoretical and practical studies. In this paper, firstly, we study the decomposition of soft sets in detail. Later, we introduce the concepts of αupper, α-lower, α-intersection and α-union for soft matrices and present some decomposition theorems. Some of these operations are set-restricted types of existing operations of soft sets/matrices, others are α-oriented operations that provide functionality in some cases. Moreover, some relations of decompositions of soft sets and soft matrices are investigated and the newfound relations are supported with numerical examples. Finally, two new group decision making algorithms based on soft sets/matrices are constructed, and then their efficiency and practicality are demonstrated by dealing with real life problems and comparison analysis. By using these proposed approaches, solutions can be presented to soft set-based multi-criteria decision making problems, both ordinary and involving primary assessments. These allow to handle soft set-based multi-criteria decision making from different perspectives.
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
This paper focuses on the set-oriented operations and set-oriented algebraic structures of soft s... more This paper focuses on the set-oriented operations and set-oriented algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties of $\alpha$-intersection of soft set are investigated, where $\alpha$ is a non-empty subset of the universal set. Later, by using $\alpha$-intersection of soft set, the notion of set-generated soft subring of a ring is introduced. The generators of soft intersections and products of soft subrings are given. Some related properties about generators of soft subrings are investigated and illustrated by several examples.
Kırıkkale Üniversitesi, 2001
Filomat, 2018
In this paper, we firstly introduce bijective soft matrix theory and research its operations, pro... more In this paper, we firstly introduce bijective soft matrix theory and research its operations, properties and algebraic structures in detail. Also, we present a bijective soft decision system based on the bijective soft matrix theory. Moreover, we construct a multi-bijective linguistic soft decision system by employing the matrices corresponding to the bijective soft sets generated from the linguistic variable parameters. Finally, the system?s decision algorithm and its application for a decision making problem are given. By using the algorithm, we determine both the linguistic variables according to the parameters and the parameters affecting the optimal choice according to the highest linguistic decision value.
More on Prime, Maximal and Principal Soft Ideals of Soft Rings
New Mathematics and Natural Computation, 2021
In this paper, we aim to extend the studies [M. R. Alimoradi, R. Rezaei and M. Rahimi, Some notes... more In this paper, we aim to extend the studies [M. R. Alimoradi, R. Rezaei and M. Rahimi, Some notes on ideals in soft rings, Journal Australian Journal of Basic and Applied Sciences 6(3) (2012) 717–721; F. Koyuncu and B. Tanay, Some soft algebraic structures, Journal of New Results Science 10(2016) 38–51] as regards maximal, prime and principal soft ideal of soft rings, characterize soft rings with these soft ideals and also provide some more relations between maximal, prime and principal soft ideals of soft rings. The notions of maximality and primeness points of soft ideals of a soft rings are defined, maximal and prime idealistic soft rings as well as maximal, prime and principal soft ideal of soft rings and their basic properties are more investigated under certain conditions, especially by means of homomorphism and epimorphism of rings. We apply some of the basic results about maximal ideals and prime ideals in classical abstract algebra to maximal, prime and principal idealistic...
In this paper, we characterize semisimple semigroups, duo semigroups, right (left) zero semigroup... more In this paper, we characterize semisimple semigroups, duo semigroups, right (left) zero semigroups, right (left) simple semigroups, semilattice of left (right) simple semigroups, semilattice of left (right) groups and semilattice of groups in terms of soft union semigroups, soft union ideals of semigroups. Moreover, we define soft normal semigroups and give some characterizations of semigroups with soft normality.
Mathematical Sciences Letters, 2018
Molodtsov introduced the concept of soft sets, which can be s een as a new mathematical tool for ... more Molodtsov introduced the concept of soft sets, which can be s een as a new mathematical tool for dealing with uncertainty. In this paper, we introduce and study soft subnear-rings, so ft ideals and soft N-subgroups of near-rings by using Molodtsov’s definition of the soft sets. Some related properties are investigated a nd illustrated by a great deal of examples.
Proceedings of the 23rd International Academic Conference, Venice, 2016
Soft matrices was firstly defined by Çağman and Enginoğlu [3]. These are representations of soft ... more Soft matrices was firstly defined by Çağman and Enginoğlu [3]. These are representations of soft sets, introduced by Molodtsov [1], for modelling vagueness and uncertainties inherent in the problems of engineering, physical science, biological science, economics, social science, medical science, etc. Çağman and Enginoğlu [3], presented a decision making method, called soft max-min decision making method, by using the concept of soft matrix. In this study, firstly, we define two new soft matrix operations and obtain some of their properties. Secondly, we construct a new decision making method by using soft matrices. The soft decision making we constructed in this study is more practical among the other decision making methods and can be successfully applied to many problems that contain uncertainties. Finally, two applications of decision making problems in which it is necessary to use these new soft matrix operations, are presented. Since this decision making method constructed on soft matrices, then it can be easily transferred to a computer.
On Near-Rings with Soft Union Ideals and Applications
New Mathematics and Natural Computation, 2021
In this paper, we define soft union near-ring on a soft set by using soft sets, inclusion relatio... more In this paper, we define soft union near-ring on a soft set by using soft sets, inclusion relation and union of sets. This new notion functions as a bridge among soft set theory, set theory and near-ring theory. We then derive its basic properties and investigate the relationship between soft intersection near-ring and soft union near-ring. Furthermore, we obtain some analog of classical near-ring theoretic concepts for soft union near-ring and give the applications of soft union near-ring to near-ring theory.
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Papers by akın osman atagün