Kernels and closures of soft set relations, and soft set relation mappings

Abstract: In this paper, the views of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SS relation are initially presented, respectively. Then, their correct calculation formulae and a few laws are received. Finally, SS relation function and inverse SS relation functions are introduced, and some related conditions are discussed.

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Algebraic and topological structures based on novel soft set relations

Journal of Intelligent & Fuzzy Systems ◽

10.3233/ifs-141356 ◽

2015 ◽

Vol 28 (2) ◽

pp. 747-756 ◽

Cited By ~ 2

Author(s):

Min Zhou ◽

Shenggang Li

Keyword(s):

Soft Set ◽

Topological Structures ◽

Set Relations

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A Method for Decision Making Problems by using Graph Representation of Soft Set Relations

Intelligent Automation & Soft Computing ◽

10.31209/2018.100000006 ◽

2018 ◽

pp. 1-8

Author(s):

Nazan Polat ◽

Gözde Yaylali ◽

Bekir Tanay

Keyword(s):

Decision Making ◽

Soft Set ◽

Graph Representation ◽

Set Relations

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Categorical Properties of Soft Sets

The Scientific World JOURNAL ◽

10.1155/2014/783056 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Min Zhou ◽

Shenggang Li ◽

Muhammad Akram

Keyword(s):

Set Theory ◽

Soft Set ◽

Soft Sets ◽

Categorical Theory ◽

Categorical Properties ◽

Topological Construct ◽

Categorical Framework ◽

Set Relations ◽

Cartesian Closed ◽

Injective Hulls

The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the categorySFunof soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find thatSFunis both a topological construct and Cartesian closed. The categorySRelof soft sets andZ-soft set relations is also characterized, which shows the existence of the zero objects, biproducts, additive identities, injective objects, projective objects, injective hulls, and projective covers. Finally, by constructing proper adjoint situations, some intrinsic connections betweenSFunandSRelare established.

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