A note on soft near-rings and idealistic soft near-rings

Sezgin, Aslıhan; Atagün, Akın Osman; Aygün, Emin

doi:10.2298/fil1101053s

Cited by 51 publications

(26 citation statements)

References 20 publications

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“…Since its inception, it has received much attention in the mean of algebraic structures such as groups [2], semirings [12], rings [1], BCK/BCIalgebras [14,15,16], d-algebras [17], ordered semigroups [18], BL-algebras [29], BCH-algebras [19] and near-rings [26]. Moreover, Xiao et al [28] proposed the notion of exclusive disjunctive soft sets and studied some of its operations and Gong et al [13] studied the bijective soft set with its operations.…”

Section: Introductionmentioning

confidence: 99%

Soft Union Ring and its Applications to Ring Theory

̧ay¹,

Sezgin²

2016

IJCA

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In this paper, soft union ring (SU-ring) on a soft set is defined by using union operation of sets. This new concept shows how a soft set effects on a ring structure in the mean of union and inclusion of sets and from this overview, it functions as a bridge among soft set theory, set theory and ring theory. Then, its basic properties are derived and the relationship between soft intersection ring defined in [N. Ç agman and F. Ç ıtak and H. Aktaş, Soft intrings and its algebraic applications, Journal of Intelligent and Fuzzy Systems, 28 (3): 1225-1233(2015] and SU-ring are investigated. Furthermore, we give the applications of SU-ring to ring theory. General Terms 2010

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Section: Introductionmentioning

confidence: 99%

Soft Union Ring and its Applications to Ring Theory

̧ay¹,

Sezgin²

2016

IJCA

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“…This is in accordance with the way that humans use to treat uncertain concepts in their daily life. In recent years, soft set theory has been applied to various kinds of algebraic structures [5,6,7,8,9,10,11,12,13,14,17,15,16,18,19,20,21]. But so far as we know, the algebras which have been investigated in virtue of soft sets are all associative, and very little attention has been paid to non-associative algebraic structures in the literature.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy soft set approach to ideal theory of regular AG-groupoids

Feng

Khan

Leoreanu-Fotea

et al. 2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∈γ, ∈γ ∨q δ )-fuzzy soft left ideals (right ideals, bi-ideals and quasiideals) over AG-groupoids and explore some related properties. Moreover, we give a number of characterizations for regular AG-groupoids by virtue of various types of fuzzy soft ideals over them.

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“…In [16], Kazancı et al used the concept of soft set to BCH-algebras. Sezgin et al studied soft nearrings [17]. C .…”

Section: Introductionmentioning

confidence: 99%

Bipolar fuzzy soft sets and its applications in decision making problem

Abdullah

Aslam

Ullah

2014

Journal of Intelligent &Amp; Fuzzy Systems

128

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In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

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A note on soft near-rings and idealistic soft near-rings

Abstract: 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 this paper, we apply the definitions proposed by Ali et al. [M.

Cited by 51 publications

References 20 publications

Soft Union Ring and its Applications to Ring Theory

Soft Union Ring and its Applications to Ring Theory

Fuzzy soft set approach to ideal theory of regular AG-groupoids

Bipolar fuzzy soft sets and its applications in decision making problem

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