Transitive closures and orderings on soft sets

In this paper first we define a partial order on a soft set (F, A) and introduce some related concepts. Then using the concept of a soft mapping introduced by Babitha and Sunil [Comput. Math. Appl., 60 (7) (2010), 1840-1849], a soft version of Knaster-Tarski fixed point theorem is obtained. Some examples are presented to support the concepts introduced and the results proved herein. As an application of our result, we show that the soft Knaster-Tarski fixed point theorem ensures the existence of a soft common fixed point for a commuting family of order-preserving soft mappings.

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“…Motivated by the work of Babitha and Sunil [5], we get the following slight invariant of the concept of a soft mapping.…”

Section: Example 116mentioning

confidence: 99%

A soft version of the Knaster–Tarski fixed point theorem with applications

Leyew

Abbas

2017

J. Fixed Point Theory Appl.

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“…Definition 6.1. [4] Let (F A , τ) be a soft topological space. If for every α 1 , α 2 in F A with α 1 / = α 2 there exists F B 1 ∈ṽ(α 1 ) and F B 2 ∈ṽ(α 2 ) such that Proof.…”

Section: Soft Separation Axiomsmentioning

confidence: 99%

“…As a continuation of their work, Yang and Guo [11] defined on soft set theory the notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a soft set relation. Moreover transitive closure of soft set relation and ordering on soft set is defined by Babitha and Sunil [4].…”

Section: Introductionmentioning

confidence: 99%

Studies on soft topological spaces

Babitha

John

2015

Journal of Intelligent &Amp; Fuzzy Systems

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Soft set is a completely generic mathematical tool for modeling uncertainties. Topology is a branch of mathematics, whose concepts exist not only in almost all branches of mathematics, but also in many real life applications. This paper mainly focuses on soft continuous functions and soft product topology. The concept soft homeomorphism and soft subbasis is also introduced and results based on these concepts are also obtained. It is also introduced the concept of soft connectedness and soft compactness. Moreover separation axioms on soft topological space are also studied and derived some relationship among these concepts.

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“…Maji et al [7] introduced many operators for soft set theory. Furthermore, some structures as cartesian product, soft set relation and orderings on soft sets was introduced by Babitha and Sunil [2,3]. Moreover, Tanay and Yaylalı improved orderings on soft sets by giving new definitions and proving new theorems on some soft structures such as directed complete soft sets and way below soft set relation [12,17,16,13].…”

Section: Introductionmentioning

confidence: 99%

Results on soft continuous functions in the soft topological spaces equipped with soft Scott topology

Yaylalı¹,

Tanay²

2017

J. Nonlinear Sci. Appl.

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In this study, some properties of soft Scott topology are examined and some relations between soft Scott topology and way below soft set relations are shown. Also the notion of soft Scott continuous function on soft topological spaces, which is equipped with soft Scott topology, is defined by focusing on the structure of the continuity of soft function and some examples are illustrated. Besides these, least fixed point theorem is proved for soft Scott continuous functions.

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Transitive closures and orderings on soft sets

Cited by 42 publications

References 12 publications

A soft version of the Knaster–Tarski fixed point theorem with applications

A soft version of the Knaster–Tarski fixed point theorem with applications

Studies on soft topological spaces

Results on soft continuous functions in the soft topological spaces equipped with soft Scott topology

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