Yazar "Atagun, Akin Osman -- 0000-0002-2131-9980" için listeleme
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A completely new view to soft intersection rings via soft uni-int product
Sezgin, Aslihan; Cagman, Naim; Atagun, Akin Osman (ELSEVIER SCIENCE BV, 2017)In this paper, we make a completely new approach to the classical ring theory via soft set theory, with the concept of soft intersection rings, ideals, (generalized) bi-ideals, interior ideals and quasi-ideals. Particularly, ... -
A New Kind of Vector Space: Soft Vector Space
Sezer, A. Sezgin; Atagun, A. O. (SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS, 2016)Molodtsov introduced the concept of soft sets. In this paper, we present the definition of soft vector spaces and construct some basic properties by using vector spaces and Molodtsov's definition of soft sets. We introduce ... -
A NOTE ON SOFT NEAR-RINGS AND IDEALISTIC SOFT NEAR-RINGS
Sezgin, Aslihan; Atagun, Akin Osman; Aygun, Emin (UNIV NIS, FAC SCI MATH, 2011)Molodtsov introduced the theory of soft sets, which can be seen as an effective mathematical tool to deal with uncertainties, since it is free from the difficulties that the usual theoretical approaches have troubled. In ... -
On operations of soft sets
Sezgin, Aslihan; Atagun, Akin Osman (PERGAMON-ELSEVIER SCIENCE LTD, 2011)Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan's law hold in soft set theory with respect to ... -
Soft groups and normalistic soft groups
Sezgin, Aslihan; Atagun, Akin Osman (PERGAMON-ELSEVIER SCIENCE LTD, 2011)Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Aktas and Cagman ... -
Soft Intersection Interior Ideals, Quasi-ideals and Generalized Bi-Ideals; A New Approach to Semigroup Theory II
Sezer, Aslihan Sezgin; Cagman, Naim; Atagun, Akin Osman (OLD CITY PUBLISHING INC, 2014)In this paper, we define soft intersection interior ideals, quasi-ideals and generalized bi-ideals of semigroups, obtain their properties and give the interrelations of them. Moreover, we characterize regular, intra-regular, ... -
Soft intersection near-rings with its applications
Sezgin, Aslihan; Atagun, Akin Osman; Cagman, Naim (SPRINGER, 2012)In this paper, we first define soft intersection near-ring (soft int near-ring) by using intersection operation of sets. This new notion can be regarded as a bridge among soft set theory, set theory and near-ring theory, ... -
Soft Intersection Semigroups, Ideals and Bi-Ideals; a New Application on Semigroup Theory I
Sezer, Aslihan Sezgin; Cagman, Naim; Atagun, Akin Osman; Ali, Muhammed Irfan; Turkmen, Ergul (UNIV NIS, FAC SCI MATH, 2015)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, ... -
Soft substructures of rings, fields and modules
Atagun, Akin Osman; Sezgin, Aslihan (PERGAMON-ELSEVIER SCIENCE LTD, 2011)tool to deal with uncertainties. In this paper, we introduce and study soft subrings and soft ideals of a ring by using Molodtsov's definition of the soft sets. Moreover, we introduce soft Soft set theory, proposed by ... -
Union soft substructures of near-rings and N-groups
Sezgin, Aslihan; Atagun, Akin Osman; Cagman, Naim (SPRINGER, 2012)In this paper, we introduce union soft subnear-rings and union soft ideals of a near-ring and union soft N-subgroups and union soft N-ideals of an N-group by using Molodtsov's definition of soft sets and investigate their ...