Soft set relations and functions

Babitha, K. V.; John, Sunil Jacob

doi:10.1016/j.camwa.2010.07.014

Cited by 265 publications

(148 citation statements)

References 10 publications

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“…Definition 2.11. [2] Let (F , A ) and (G , B ) be two soft sets over U , then the cartesian product of (F , A ) and [5]) A binary soft set relation R on (F , A ) which is reexive, antisymmetric and transitive is called a partial ordering of (F , A ) . The triple (F , A , ) is called a partially ordered soft set or posset i.e a posset consists of two things, a soft set (F, A) and the partial ordering  Suppose (F , A , ) is a posset.…”

Section: Volumementioning

confidence: 99%

Continuity of Partially Ordered Soft Sets via Soft Scott Topology and Soft Sobrification

Sayed

2014

BMSA

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This paper, based on the concept of partially ordered soft sets (possets, for short) which proposed by Tanay and Yaylali [23], we will give some other concepts which are developing the possets and helped us in obtaining a generalization of some important results in domain theory which has an important and central role in theoretical computer science. Moreover, We will establish some characterization theorems for continuity of possets by the technique of embedded soft bases and soft sobrification via soft Scott topology, stressing soft order properties of the soft Scott topology of possets and rich interplay between topological and soft order-theoretical aspects of possets. We will see that continuous possets are all embedded soft bases for continuous directed completely partially ordered soft set (i.e., soft domains), and vice versa. Thus, one can then deduce properties of continuous possets directly from the properties of continuous soft domains by treating them as embedded bases for continuous soft domains. We will see also that a posset is continuous if its soft Scott topology is a complete completely distributive soft lattice.

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Section: Volumementioning

confidence: 99%

Continuity of Partially Ordered Soft Sets via Soft Scott Topology and Soft Sobrification

Sayed

2014

BMSA

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“…There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. So, the properties and applications of soft set theory have been studied increasingly [1,2,4,5,6,7,15,18,19,20,21]. Matrices play an important role in the broad area of science and engineering.…”

Section: Introductionmentioning

confidence: 99%

The Parameterization Reduction of Soft Point and its Applications with Soft Matrix

Şenel¹

2017

IJCA

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The innovation about soft point in this study is, soft point's soft matrix form which were not described before is defined for each set of parameters. The matrix representation of soft points is useful for storing all soft points that can be obtained in all different parameters. The proposed soft matrix provides every soft point that changes with each parameter that takes place in a soft set is proved and showed that it enables detailed examination in application of soft set theory. General Terms 2010 AMS Classification: 03G25,20D05Keywords Soft set, soft point, soft matrix, soft matrix form of soft point.

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“…Recently, Molodtsov [11] introduced the soft set as a mathematical tool for dealing information as the uncertainty of data in engineering, physics, computer sciences and many other diverse field. Presently, the soft set theory is making progress rapidly [1,4]. Pawlak's rough set [12,13] can be viewed as a special case of soft rough sets [4].…”

Section: Introductionmentioning

confidence: 99%